Question

Simplify the following, using the rules of exponents

i) x9. x8

ii) x5 . x-9

iii) x-11. x

iv) x6 . x0.15

v)𝑥5/𝑥−3

vi)𝑥−4/𝑥−7

vii)𝑥−3/𝑥−4

viii)𝑥9/√𝑥

ix) (𝑥−4)−5

x) (𝑥−0.4)−2

xi)1/𝑥−1.5. 1/𝑦−2.5

xii)𝑥−3.5/𝑦−2.2

Answer 1

Following below are some common rules of exponent:

1. Product rule$= a^m ×an^ = a^{m+n}$

2. Division rule $= a^m÷a^n = a^{m−n}$

3. Zero exponents $= a^0 = 1$

4. Negative exponents $= a^{−m} = \frac{1}{a^m}$

$i) x^9. x^8\\ = X^{9+8}\\ = X^{17}$

$ii) x^5. x^{−9}\\ = X^{5+(−9)}\\ = X^{5−9}\\ = X^{−4}$

$iii) x^{−11}. x \\ = X^{−11+1}\\ = X^{−10}$