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Powers

Bases (positive real numbers) : a, b

Powers (rational numbers) : n, m

1. a⁰ = 1

Example:

2⁰ = 1

2. a¹ = a

Example:

2¹ = 2

3. (a^m)ⁿ = (aⁿ)^m = a^mn

Example:

(a³)2 =a⁶

4. a^m.aⁿ = a^m+n

Example:

2¹.2² =2⁽¹⁺²⁾

=2³

=8

5. a^-m = 1/a^m

Example:

4⁻³= 1/4³

= 1/64

6. a^m/aⁿ = a^m-n = 1/a^n-m

Example:

2³/2¹ =2^(3-1)

= 2²

= 4

7. (ab)ⁿ = aⁿbⁿ

8. (a/b)ⁿ = aⁿ/bⁿ

9. a^m/n= ⁿ√a^m

10. (a^mbⁿ)^x=a^mxb^nx

Example:

\( (x^3\cdot y^4)^2 =x^{3\cdot 2} \cdot y^{4\cdot 2} \)

\( (x^3\cdot y^4)^2 =x^6 \cdot y^8 \)