Laws of Exponents

1. LAWS OF
EXPONENTS
- Ruby Rose Ann B. Panganod

2. PRODUCT OF POWERS
𝑎 𝑚
. 𝑎 𝑛
= 𝑎 𝑚+𝑛

3. PRODUCT OF POWERS
𝑎3
. 𝑎2
= 𝑎3+2
= 𝑎5
EXAMPLES:
21. 21 = 21+1 = 22
(𝑥 + 𝑦)3
. (𝑥 + 𝑦)5
= (𝑥 + 𝑦)3+5
= (𝑥 + 𝑦)8

4. POWER OF A POWER
(𝑎 𝑚
) 𝑛
= 𝑎 𝑚𝑛

5. POWER OF A POWER
(𝑎3
)2
= 𝑎3.2
= 𝑎6
EXAMPLES:
(25)1= 25.1 = 25
((𝑥 + 𝑦)4
)5
= (𝑥 + 𝑦)4.5
= (𝑥 + 𝑦)20

6. POWER OF A PRODUCT
(𝑎𝑏) 𝑚
= 𝑎 𝑚
𝑏 𝑚

7. POWER OF A PRODUCT
(𝑎𝑏)3
= 𝑎3
𝑏3
EXAMPLES:
(𝑥𝑦)5 = 𝑥5 𝑦5
(2𝑥2
)3
= 23
𝑥6

8. QUOTIENT OF POWERS
𝑎 𝑚
𝑎 𝑛 = 𝑎 𝑚−𝑛

9. QUOTIENT OF POWERS
EXAMPLES:
𝑎4
𝑎2
= 𝑎4−2 = 𝑎2
𝑥5
𝑦7
𝑥2 𝑦4
= 𝑥5−2
𝑦7−4
= 𝑥3
𝑦3

10. POWERS OF QUOTIENT
𝑎
𝑏
𝑚
=
𝑎 𝑚
𝑏 𝑚

11. POWERS OF QUOTIENT
EXAMPLES:
𝑥
𝑦
3
=
𝑥3
𝑦3
𝑥2
𝑦4
3
=
𝑥6
𝑦12