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LAWS OF EXPONENTS
By Patrica Hensley - Jefferson Davis Campus

LAW

EXAMPLE

1. xm xn = x m + n

23 · 25 = 28 = 256
x2 · x3 = x5

2. x0 = 1 if x ¹ 0

20 = 1

3. x-n = 1/xn

2-3 = 1/23 = 1/8

4. 1/x-n = xn

1/2-3 = 23 = 8; 1/x-5 = x5

5. xm / xn = x m-n = 1/ x n-m

212 / 28 = 24 = 16; x8 / x12 = 1/x4

6. xm / xm = 1

24 / 24 = 1

7. (xm)n = x mn

(23)5 = 215 ; (x2)3 = x6

8. (xy)n = xn yn

(2 · 4)3 = 23 · 43 = 8 · 64

9. (x/y)n = xn / yn

(2/3)3 = 23/33; (1/3)5 = 1/ 35 = 3-5

10.(x/y)-n = (y/x)n

(3/4)-2 = (4/3)2 = 16/9