Definitions and Rules for Exponents

Definitions and Rules for Exponents

For all integers m and n and all real numbers a and b, the following rules apply.

Product Rule a^m.aⁿ = a ^m+n

Quotient Rule $\frac{a^{}m}{a^{n}}$ = a^m-n(a ≠ 0)

Zero Exponent a⁰ = 1 (a ≠ 0)

Negative Exponent a ^–n = $\frac{1}{a^{n}}$ (a ≠ 0)

Power Rules (a^m)ⁿ= a^mn

(ab)^m = a^mb^m

$(\frac{a}{b})^{m}= \frac{a^{m}}{b^{m}} (b \neq 0)$

Special Rules $\frac{1}{a^{-n}} = a^{n}(a \neq 0) \frac{a^{-n}}{b^{-m}} = \frac{b^{m}}{a^{n}} (a,b\neq 0)$

$a^{-n} = (\frac{1}{a})^{n}(a\neq 0)(\frac{a}{b})^{-n}=(\frac{b}{a})^{n}(a,b\neq 0)$