Law of indices exercise dse pdf. Nov 16, 2021 · Language: Malay (ms) ID: 1648604.

Simplify the following expressions and write the answers in positive indices. This document provides a mathematics exercise on inequalities for the HKDSE. com/forms/d/1gwuTCvji-GdAzpHOGRjPKLskgFvscbOA0vUsB8AuDlE/viewform?edit 2. When different absorbers are put in between, the corresponding corrected count rates are recorded. Help you improve DSE Math result efficiently. May 31, 2013 · Key points include laws of indices, rationalizing surds, laws of logarithms including change of base, and the general forms of exponential functions as ax and ex. (a) + x6z 230 (b) 322. Downloadable version. 00 am (2 hours 30 minutes) This paper must be answered in English GENERAL INSTRUCTIONS 1. pdf) and the using a computer leaflet (. 唔好以為唔駛考 >. 432 Laws of Indices for Multiplying Powers. Laws of Indices Video 174 on Corbettmaths Question 1: Write as a single power of 2. Write 3x+y in terms of. Dedicated to S4 - S6 students. Using all 3 laws of indices . resulting from a moving conductor in a steady magnetic field or a stationary conductor in a changing magnetic field. A certain radioactive source gives a corrected count rate of 300 counts per minute. Powers, or indices We write the expression 3 ×3 ×3 Worksheet 1:8 Power Laws Section 1 Powers In maths we sometimes like to nd shorthand ways of writing things. Quadrilaterals 8. 4 2 9 a− ( ) a More Support Sep 26, 2019 · Books. Multiplication 乘法 a ×a =am +n 2. a m ÷ a n = a m – n 3. am ÷ an = am − n. The 3 is called the index. a0 ap. 8 Factorization of Polynomials p. Country: Malaysia. ppt / . 9. 16/11/2021. From the information given in paragraphs 3 and 4, decide if the following statements are true (), false (F) or T not given (NG). Madas Created by T. The difference ofthe number of male applicants and the number of female applicants is 91 (4 marks) Find the number of male applicants in the recruitment exercise. Answer your questions online. Madas Question 11 Write each of the following expressions as the sum of terms of the form kx n, where k is a constant. (A) Common Law of Indices 常用指數定律 Common Law of Indices 常用指數定律 1. a 2 1 4/9 – 12/9 Unit 2: Laws of integral indices 2. 17 Simultaneous Linear Equations in unknowns 911 – 9 = 92. 8. : DSE Target (DSE 坐 1 望 精選 ) CONTENT Law of Indices p. Index questions are provided here to help students understand how to simplify expressions using simple formulas and techniques. Laws of indices video. Giving your answers in standard form, correct to 3 significant fi. Let us have a look at some of the topics that are being discussed in this chapter. Applications in Trigonometry 11. Apply the fractional index outside the brackets to everything inside the brackets. This means: PP-DSE-ENG LANG 1-A-QAB–2. mc-bus-lawsindices-2009-1. In this leaflet we remind you of how this is done, and state a number of rules, or laws, which can be used to simplify expressions involving indices. School subject: MATHS (1126772) Main content: Maths (2011589) From worksheet author: CHAPTER 3 INDICES MATHEMATICS FORM 3. Write the following expressions in order, starting with the smallest. School subject: Math (1061955) Main content: Indices (1990626) From worksheet author: applying the Laws. 5 2 13/9 – 20/9 2. Also find all West Bengal Board Chapter Notes, Books, Previous Year Question Paper with Solution, etc. 1. If , find x and y, where a, b are different positive primes. pdf) Advice for students. Alternative versions The laws of indices Introduction A power, or an index, is used to write a product of numbers very compactly. Examples: 1) 2) 3) Power Law/ Power Rule – When an expression is raised to a certain index and is raised again to another index, the indices (m and n) are multiplied. Indefinite integrals and their applications. Powerpoint presentation overviewing Indices for the GCSE syllabus. Paper. Powers,orindices Index Laws Mathematics IMA Intro. dsemth. Example: X 3 x X 2 = ( X x X x X) x (X x X) = X 5. Country: Indonesia. and b. Maths I Index laws are the rules for simplifying expressions involving powers of the same base number. 13 Linear Inequalities p. Jan 27, 2021 · Country code: GY. Oct 25, 2022 · 25/10/2022. 6. 1 Without a calculator, find the value of . /current. Apr 24, 2020 · Laws of indices. Solution: We proceed with the following manipulation –. 等我地一齊嚟重溫一吓…. The exponent of a number says how many times to use the number in a multiplication. 3 understand the definition and properties of D. f. Smart Exercise, the most effective ever. Absorber. 2a2b Simplify the following. 2 Zero and Negative Integral Indices We are now going to extend the idea of exponents to zero and negative integral indices in such a way that the laws of indices hold for all integral indices. CHEMISTRY PAPER 1. 1 Introduction. More about 3-D Figures 9. 2 Find the value of in the following expressions: (a) (b) Working: (a) Getting Pass Tutorial for DSE Class: _____ Tutorial 1 Laws of Integral Indices Key Points Laws of Integral Indices If m, n are integers, and a, b 0, then 1. Cost only one tutorial lesson fee per month. Index or Indices refers to the powers of a number or variable. Sep 2, 2019 · Previous: Distance Time Graphs Practice Questions Next: Negative Indices Practice Questions GCSE Revision Cards Introduction. laws. Question 1: Show that for any positive real number p, the expression a−p is equivalent to 1 ap. Write 32y in terms of b. 7 3 y y g. A number of the form a m where a is a real number, a is multiplied by itself m times. th. (k3)2 = k3 2×= k6 Law (4): (ab)n = anbn e. If a, b 0 and m, n are both integers, then. Laws of indices worksheets. Write 3x+1 in terms of. Zero index 零指數 0a =1 (a ≠0) 5. am + nSecond Index Law: When terms with the same base are divided, the indices are sub. • You must show all your working out. If (p + q)-1 (p-1 + q-1) = paqb, prove that a + b + 2 = 0, where p and q are different positive primes. Changing the subject of a formula (6 exercises) 8. Sep 18, 2019 · Next: Multiplying Terms Textbook Exercise GCSE Revision Cards. 指數定律 (Law of Indices) 基本上每年DSE考試MC同短題目都有出指數定律、仲要考嘅嘢年年都一樣。. p p3 × d. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Primary Study Cards. Country code: MY. mn a +. a0 =1 Revision Exercise Short Questions 1. x x4 3× b. 10. Mar 23, 2019 · HKDSE 2018 Mathematics (Compulsory Part) Paper 2 Question 18^2n+1 / 4^3n+1 = (2^3)^2n+1 / (2^2)^3n+1= 2^6n+3 / 2^6n+2= 2^6n+3-(6n+2)= 2^6n+3-6n-2= 2ANS: B【La Apr 4, 2018 · Previous: Fractional Indices Practice Questions Next: Limits of Accuracy Practice Questions GCSE Revision Cards Feb 9, 2014 · 中三數學重點一：指數法則 Laws of Indices-----指數法則是中三其中一重點課題。基礎打得唔穩﹐便會環環相扣 Oct 30, 2018 · 第六集《目擊個案 中集》類似犯案手法, 次次一樣先拆穿, 然後factorize, 再約簡,最後按數機答案好多時都是個數字睇埋下一集 Unit 3 Section 2 : Laws of Indices. K206d: Laws of indices for multiplying and dividing powers. Other contents: Exponents. 80. Six Corbettmaths - This video goes through the laws of indices needed for both the foundation and higher tiers. a m×an = a +n First Index Law (am)n = amn Second Index Law am an = am−n Third Index Law a−m = 1 am a0 = 1 a1 n = n √ a Examples: Simplify the following expressions, leaving only positive indices Jan 12, 2021 · Country: Bahamas. School subject: Math (1061955) Main content: Exponents (2011533) From worksheet author: The Live Worksheet exercise of Indices for Year 9. apply Lenz’s law to determine the direction of induced e. Laws of Indices 3. Answers written in the margins will not be marked. google. 434 Laws of Indices for Raising a Power to a Power. ()am n =amn, ii. ( 中文版下載) ( English Version download) Ch2 More about Percentages續百分法. There are three rules that should be used when working with indices: 1. Simplify 4 5 7 xy− x and express your 1. They are called the Miller indices of the face. ( 中文版下載) ( English Version download) Ch3 More about The laws of indices Introduction When a number is to be multiplied by itself a power, or an index, can be used to write this compactly. Applications of differentiation. ( a b) n = a n b n 5. Powers of quotients. 2 Zero and Negative Indices 2. y y5 2× c. = 3x and b = 3y. (ab)n =anbn 5. to Fin. com/forms/d/1gwuTCvji-GdAzpHOGRjPKLskgFvscbOA0vUsB8AuDlE/viewform?edit Exercise 4 IR and UV English version Chinese version Exercise 5 Electromagnetic spectrum English version Chinese version . ( a b) n = a n b n. Example questions demonstrate working with indices, simplifying surds, solving logarithmic and exponential equations using appropriate logarithm laws and change of variable techniques. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". express the big number as a power of the smaller number Unit test. Level 4+ Guarantee and Level 5** award. 1 Laws of Indices for the Edexcel A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. If a, b are real numbers (>0, ≠ 1) and m, n are real numbers, following properties hold true. The radius of the earth is 6 . Mar 24, 2021 · 1) 2) 3) Division Law/ Quotient Rule – When expressions with the same base (x) are divided, the indices (m and n) are subtracted. The number a is called the base and the super script m is called the index (plural indices) or exponent. Country code: ID. When a number is to be multiplied by itself a power, or an index, can be used to write this compactly. 1 Concepts of inequalities Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you. (m)n =a mn 4. Nov 16, 2021 · Language: Malay (ms) ID: 1648604. 1 understand the definitions of rational indices 16 The definitions include and . Exercise 5: Subject on both sides. 同學最緊要係識得利用上面幾條公式嚟化簡有指數嘅數式就可以了。. h3 × h4 = h3 + 4 = h7 Law (2): am ÷ an = m n a a = am – n e. ↓. Abundant study resources. A3. Ch1 Laws of Integral Indices指數定律. Division 除法 m n n m a a a = − 3. m. Performing operations on numbers or pronumerals written in index form requires the application of the ind. m m m b a b a ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ (b ≠0) 4. 310. Sep 7, 2019 · 本集內容包括：－ Laws of Integral Indices「整數指數律」－ Examples of Laws of Integral Indices 「整數指數律」－ Scientific Notation「科學記數法」－ Example using E 31. −1 < x < 0. This document contains 14 multi-part physics problems about Newton's laws of motion involving forces, masses, accelerations, and inclines. The plural of index is indices. Law 2To divide any two real numbers in index form that have the same base, subtract the powers or indices of the denominator from those of the numerator, and raise the base to. 1–8] 1. • Answer all Questions. a−p = a(0–p) Using Law 2 i. examine induced e. You can 'verify' them with particular examples as below, but this is not a proof: or, Created by T. Revision notes on 2. It also explains why any number/variable to the power of zero is one. Powers, or indices We write the expression 3×3× 3 5H Revision on Indices Rules of Indices: a a am n m n× = + and a a am n m n÷ = − and ( ) a am mnn = Negative and fractional indices: n 1 n a a − = and 1 a an = n and ( ) m m a a or an = n n m Special indices: a a1 = and a0 =1 1. ML Aggarwal Solutions for Class 9 Maths Chapter 8 Indices is designed by individual subject experts at BYJU’S, to help students solve the exercise problems of the chapter. (b) 3a4 X 9a5 (x-2)4 (c) (d) . Other contents: zero, negative, multiplication and division power Law. Law of indices for e "expanding e" quesiton 1 "expanding e" quesiton 2 Limit question 1 about e *** Limit question 2 about e *** Limit question 3 about e *** Definition of natural log Solving equations related to e. Textbook Exercise. Variables such as tension, weight, friction, and velocity are calculated. Previous: Forming Expressions Textbook Exercise Using the powers law of indices . Apply the negative index outside the brackets by 'flipping' the fraction inside the brackets. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. e. Sep 24, 2018 · Solved Examples on Laws of Indices, Exponents. Coordinate Geometry of Straight Lines 12. Negative Indices Textbook Exercise. 3 Scientific Notation 2. • Answer the Questions in the spaces provided – there may be more space than you need. Exercise 3: Two step multiplication. Examples: 3. Problems involve forces acting on objects up and down inclines, being lowered or raised by ropes or strings, and objects accelerating or slowing down along horizontal or Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost. 所以無論你諗住攞5**、定只係想攞個合格，都千奇唔好放過依幾分。. ( a m) n = a m × n 4. Mixed indices. Conditional probability and independence. We would like to show you a description here but the site won’t allow us. Basic Laws of Indices. S3 Math exercise Free PDF download 中三數學練習免費PDF下載 Laws of indices: when multiplying, add the indices when dividing, subtract the indices when raised to a power, multiply the indices Zero index: any number or letter to the power of 1 is zero Negative indices: “1 over…” N. • Diagrams are NOT accurately drawn, unless otherwise indicated. The document also provides the answer to each problem, solving for the range of values that Sep 26, 2019 · Previous: Indices (numerical) Textbook Exercise. 1 Simplify: (a) (b) (c) (d) (e) (f) Working: (a) E. In this leaflet we remind you of how this is done, and state a number of rules, or laws, which can be used to simplify expressions involving indices. m n n m a a a = − 3. (3 marks) 7. Scholar Investment Challenge. txt) or view presentation slides online. Then 106 means multiply 10 by itself 6 times. Consider the following patterns: 103 = 1000 23 = 8 102 = 100 22 = 4 101 = 10 21 = 2 100 = 1 20 = 1 10–1 = ? 2–1 = ? 10–2 = ? 2–2 = ? We will discuss here about the different Laws of Indices. 11 when multiplying, add the indices when dividing, subtract the indices when raised to a power, multiply the indices Zero index: a number or letter to the power of zero is 1 Negative indices: Fractional indices: n or When evaluating fractional indices, it is easier to do the root first as you then have a smaller number to square, cube etc. Exponents are also called Powers or Indices. Overview. More about Deductive Geometry 7. (a) 2² x 2² (b) 2² x 2³ (c) 2⁶ x 2² (d) 2⁴ x 2³ (e) 2⁶ x 2⁸ (f) 2² x 2 (g) 2 x 2⁴ Laws of Integral Indices. 137 Equations with Indices Starter 1. 2 understand the laws of rational indices The laws of rational indices include: qap a p= a + q q p a a p= a q (ap)q = apq pa pb = (ab)p p p b a b a 3. Country: Guyana. （所有練習只供教學用途，請勿轉售或作商業用途，如有任何版權侵犯，請立即通知本人以作下架。. They are usually small because the corresponding lattice planes are among the densest and Solutions for the assessment Indices Rules - Basics 1) a) 3 5 b) 5 × 3 2 c) 7. i. Indices Name: _____ Instructions • Use black ink or ball-point pen. In his work on the gravitational force between two bodies he foun. Laws of indices as applied to products. a m × a n = a m + n 2. Indices show where a number has been multiplied by itself, eg squared or cubed, or to show roots of numbers, eg square root. 433 Laws of Indices for Dividing Powers. 3 Handling positive, fractional, negative and zero indices The laws of indices Introduction A power,oranindex, is used to write a product of numbers very compactly. indices. Title: Print Layout - Mathster Created Date: 20140105090002Z Simplifying expressions using the laws of indices Simplifying indices. However, you should still follow the good practice outlined in the safe use of DSE guidance sheet (. x x5 2÷ f. One such shorthand we use is powers. The following table shows the results. (d) (a5b 2) Simplify the following expressions and express the answers with positive indices. 指數定律. Given that. º www. Concept of limit electromagnetic induction. Next:Inequalities Textbook Exercise. SWAE Managers Reference Guide: DSE for Hybrid Working (. Simplify the following expressions: a. It contains 16 problems solving various inequalities involving variables like x, r, t, k, u, and α and β. 3 Formulae & Change of Subject p. 27) was a mathematician, physicist and astronomer. 4 Different Numeral Systems 2 1. Exercise 6: Fractions. The cubed sign tells us to take the number and multiply it by itself 3 times. am an = a(m–n), we can rewrite the above expression as –. As an employer, you must protect your workers from the health risks of working with display screen equipment (DSE), such as PCs, laptops, tablets and smartphones. Definite integrals and their applications. 2. n n b a b a = 6. (Review of last lesson) Simplify: (a) (b) Notes An equation involving indices may look some something like this: In order to solve such an equation the base numbers must be the same. 有英文版嗎？ 有。請在畫面頂部按「用戶」圖示，然後按「設定」。在語言選項中，你可分別選擇「平台語言」及「數學語言 Jun 4, 2023 · HKDSE Maths (Core) Past Paper Solutions香港中學文憑試數學科(必修部分) 歷屆試題題解Law of Indices指數定律#dse #dsemaths #hkdse #mathstutorial #pastpapers #pastpapersolutions Law of indices quiz for 12th grade students. With fractions, flip the fraction and change the sign of the index: E. power. (–2n) 3 = (–2) 3 × n = –8n Law (5): n n n a The Chapter 7, Indices [Exponents], contains 3 exercises and the Solutions given here contains the answers for all the questions present in these exercises. 3. 2x and 6x are like terms and 2x + 6x can be simplified as (2 + 6)x = 8x 4pq2 and –pq2 are like terms and 4pq2 – pq2 can be simplified as (4 – 1)pq2 = 3pq2 6ab and 5ac are unlike terms and they cannot be simplified Factorization 1. Law 1: multiplying indices Law 2: dividing indices Law 3: brackets with indices Brackets with indices examples Law 4: power of 0 Law 5: negative indices Law 6: fractional indices (H) Laws of indices examples. Access Solution for NCERT Class 9 Mathematics Chapter Laws Of Indices including all intext questions and Exercise questions solved by subject matter expert of BeTrained. Consider the compound inequality or 5 + x > 4 (a) (b) Solve ( * ) • Feb 8, 2023 · Name: Class: No. How to use the laws of indices. It is easier to write 23 than 2 2 2. Previous:Laws of Indices (numerical) Textbook Exercise. These three results are logical consequences of the definition of an , but really need a formal proof. There is no requirement in law for students to complete a DSE assessment. Information DSE 數學 – 必修 >. pdf - Read online for free. a) (12) 2 2 3x + b) (1 12 2) Sep 18, 2019 · The Corbettmaths Textbook Exercise on the Laws of Indices. GCSE Revision Cards. pdf), Text File (. x x7 3× − e. Laws of Integral Indices (整數指數律 ) If a, b ≠ 0 and both m and n are integers, then Law (1): am × an = am + n e. From the starter, the laws of indices can be stated: when multiplying, add the indices when dividing, subtract the indices when raised to a power, multiply the indices Zero index (anything divided by itself is ): E. The Health and Safety (Display Screen Equipment) Regulations apply to workers who use DSE daily, for continuous periods of an hour or more. 5-a-day Workbooks 3. use negative and fractional indices. 5-a-day Workbooks. Data Services. Measures of Central Tendency and Other Statistical Values 6. Jan 15, 2019 · Exercise 1: Adding and Subtracting Exercise 2: Multiplying and Dividing. Corrected count rate / counts min −1. Introduction to Probability 有興趣報讀課程既同學，可以填妥以下既 Google Form：https://docs. com. The general statement of this law is: a n = a mn,where a . =. First Index Law: When terms with the same base are multiplied, the indices ar. School subject: Math (1061955) Main content: Laws of Indices (2043192) From worksheet author: Simplifying Algebraic expression under Multiplication and Division applying Laws of Indices. circumference of the earth in:mcmmmkm11. n n a a 1 − = 7. DSE Topics Supplement 1 Laws of Integral Indices, Expansion and Factorization of Polynomials Junior Sec Foundation Topics Key Review (a) Laws of Integral Indices Exercise 1A Conventional Questions Laws of Integral Indices Simplify the following expressions and express the answers with positive indices. Full refund for 14 days -½. 11. am •an =am+n 2. Common misconceptions. Jul 1, 2023 · The law of rational indices states that the intercepts, OP, OQ, OR, of the natural faces of a crystal form with the unit-cell axes a, b, c (see Figure 1) are inversely proportional to prime integers, h, k, l. Subtract the power of the term in the denominator from the term in the numerator: . B. In. Powers of products. g. Next: Laws of Indices (numerical) Textbook Exercise. 3a3 X 4a (a 3. Revision Summary of DSE Mathematics (Compulsory Part) Number and Algebra Polynomials Like terms and unlike terms e. 2 Laws of Indices [Exponents] 7. They can also be used to represent roots, such as the square root, Laws of Exponents. Search. (all in one) 149 Multiply Algebraic 有興趣報讀課程既同學，可以填妥以下既 Google Form：https://docs. 1. Level up on all the skills in this unit and collect up to 1,700 Mastery points! Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Approximation of definite integrals using the trapezoidal rule. In this article, you can practise various problems on indices of numbers, variables and some special expressions. Indices are used to show numbers that have been multiplied by themselves. a 2 − b 2 ≡ (a + b)(a − b) 2. 4 ·6 10 m. There are TWO sections, A and B, in this Paper. 5-a-day Workbooks In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. pptx), PDF File (. define magnetic flux Φ = BA cosθand weber (Wb) as a unit of magnetic flux. Introduction. 30 am - 11. − n. Try it yourself: Mar 14, 2023 · HKDSE Maths (Core) Past Paper Solutions香港中學文憑試數學科(必修部分) 歷屆試題題解Law of Indices指數定律#dse #dsemaths #hkdse #mathstutorial #pastpapers #pastpapersolutions Exercise for HKDSE (Inequalities) (3). Linear Inequalities in One Unknown 5. Click here for Questions. Sep 26, 2019 · Next: Negative Indices Textbook Exercise GCSE Revision Cards. a m • a. 6 2 h h = h6 – 2 = h4 Law (3): (am)n = am × n e. Powers 冪 i. To manipulate expressions, we can consider using the Law of Indices. LEARNING. 2 指數定律 (Laws of Indices) 指數定律基本上係指下面幾條恆等式：. 1 Laws of Positive Integral Indices 2. Negative index 負指數 m m a a 1 − Jan 22, 2024 · 中三數學練習. Provided by dse. Simulation GCSE-Indices - Free download as Powerpoint Presentation (. Sir Isaac Newton (1642-1. Percentages (II) 4. 32. Simplify the expression inside the brackets: Cancel down the constants (divide 54 by 2). Express the answers with positive indices. (ab) =ambm, iii. pdf) to avoid aches and pains Laws of Integral Indices 1. 7. 2017-DSE CHEM PAPER 1A HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2017. These laws only apply to expressions with the same base, for example, 3 4 and 3 2 can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 3 5 and 5 7 as their base differs (their bases are 3 and 5, respectively). 4 days ago · Textbook PDF: Interactive PDF (Books 5-E4), PDF with Teacher's Notes (Books 5-E4) Lesson Worksheets (Books 5, E2, E3, E4) Know More (Books 5-E3) Solution for Student's Book (Books 5-E4) Lesson Planning: Teaching Scheme and Chapter Objectives (Book 5-E4) Supplementary Materials: NSE Worksheet (Books 5, E1, E3) Multimedia Resources. [Nos. Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10. Author: fcl Created Date: . Get Instant and Historical Market Data. Other contents: Variables, basic operations, index or exponents. Area and Volume (III) 10. 5 2 0. Find other quizzes for Mathematics and more on Quizizz for free! In a recruitment exercise, the number of male applicants is 28% more than the number of female applicants. 3 mm aluminium sheet. 4 Different Numeral Systems Workbook Revision exercise 2 Unit 3: Linear inequalities in one unknown 3. a = a. Overview; App Premium DSE Preparation Plan. Exercise 4: Two step division. From this, we deduce the second. (Review of last lesson) Without a calculator, evaluate . In this example: 82 = 8 × 8 = 64. jo vg we fu vm zk wg ne ue ph