Laws of Indices This guide describes how to work with and manipulate the laws of indices in mathematics. What are indices? Indices usually appear in mathematics as a numerical superscript after a number or variable and are also known as powers or exponents. The word ‘indices’ is the plural of ‘index’. Laws of Indices This worksheet has questions about the laws of indices: which are fundamental to algebra and also play a part in numerical calculations. 1. Without a calculator, use the laws of indices to help you evaluate the following: (a) 6 4 2 (b) 91/ 32 (c) 64 1/ 3 (d) 4 28 (e) 5 3 3 3 (f) 1/4 1/2 16 4 Index Laws Mathematics IMA Intro. to Fin. Maths I Index laws are the rules for simplifying expressions involving powers of the same base number. 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 Indices or Powers mc-TY-indicespowers-2009-1 A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Mathematics (Linear) – 1MA0 ALGEBRA: INDICES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Instructions Use black ink or ball-point pen.
In 4x3, its coefficient is 4, base is x and power is 3. The power of the base of an algebraic term is also called index. The plural form of index is indices. Law of Six rules of the Law of Indices: To manipulate math expressions, we can consider using the Law of Indices. 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 4 5 and 9 7 as their base differs (their bases are 4 and 9, respectively). The laws of indices Introduction A power, or an index, is used to write a product of numbers very compactly. The plural of index is indices. 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. 1. Powers, or indices We write the expression 3×3× 3
Increasingly, difficulty in understanding algebra is proving a problem for many students as they commence studying GCSE, A level and engineering courses. When the power or index is a fraction say then and it is a surd of order n. But this will be dealt with later on. The Laws on Indices. The rules that are going to be Applying the Exponent Rule for Negative Exponents. Simplify. 1) 8−1. 2) 3−2. 3) y . −7. 4) w. −12. 5) (3x). −1. 6) (5a). −2. 7) 4c. −3. 8) 2pr. −5. 9) −6q. −2. 10) −18a. The index laws apply to fractional indices as well as positive and negative integer indices. Using the first index law we know that. 1. 1. 1. 2. 2.
Index Laws Mathematics IMA Intro. to Fin. Maths I Index laws are the rules for simplifying expressions involving powers of the same base number. 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 Indices or Powers mc-TY-indicespowers-2009-1 A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section of text you will learn about powers and rules for manipulating them through a number of worked examples. Mathematics (Linear) – 1MA0 ALGEBRA: INDICES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Instructions Use black ink or ball-point pen. Download Six Rules Of Surds in PDF. Engineering Mathematics Six Surds Rules pdf. An online surds rule printable. Rules Of Surds Print This Page Download This Page. What is Surds? Law of Indices. Fourier Series formula. More >> Physics Equation with examples Topic 4: Indices and Logarithms Lecture Notes: section 3.1 Indices section 3.2 Logarithms Jacques Text Book (edition 4): section 2.3 & 2.4 Indices & Logarithms . INDICES Any expression written as an is defined as the variable a raised to the power of the number n Indices & the Law of Indices Introduction. 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).
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. 1. Powers, or am an. = am−n. Third Index Law a−m = 1 am a0 = 1 a. 1 n = n. √ a. Examples: Simplify the following expressions, leaving only positive indices in the answer. (a) . Learning Enhancement Team. Steps into Algebra. Laws of Indices. This guide describes how to work with and manipulate the laws of indices in mathematics. This worksheet has questions about the laws of indices: which are fundamental to algebra and also play a part in numerical calculations. 1. Without a calculator