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 am.an = a m+n

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

Zero Exponent a0 = 1 (a ≠ 0)

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

 

Power Rules (am)n = amn

(ab)m = ambm

(\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)

 

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