Manipulating Indices © T Madas

A Summary on the Rules of Indices © T Madas

A Summary on the Rules of Indices 1. 2. Special Results a 0 = 1 a 1 = a 1n = 1 0n = 0 (unless n = 0) 3. 4. 5. 6. 7. 8. © T Madas

It is often required to evaluate expressions involving indices without using a calculator Typical intermediate questions: Higher tier questions: Higher tier, A* questions: © T Madas

Evaluating such expressions requires: It is often required to evaluate expressions involving indices without using a calculator Evaluating such expressions requires: Knowing the rules of indices Using them effectively Recognising certain “patterns” or “themes” Recognising small powers of 2,3,4, … , 10 © T Madas

Examples on manipulating & evaluating indices © T Madas

Examples on manipulating & evaluating indices The next 2 examples require to change the base of the power, as well as applying the rules of indices competently. © T Madas

Exam Question © T Madas

If x = 2m and y = 2n , express the following in terms of x and/or y only: 1. 2m + n 2. 23m 3. 2n – 2 1. 2m + n = 2m x 2n = x x y = xy [ ]3 2. 23m = 23 x m = 2m = x 3 1 4 y 4 3. 2n – 2 = 2n x 2-2 = 2n x = y x 1 4 = y 4 = 2n ÷ 22 = 2n ÷ 4 = y ÷ 4 = © T Madas

© T Madas