Laws of Exponents

Exponents and radicalsLaws of ExponentsProperties of Radicals Scientific Notation

Laws of exponents

Product of powers

a^{m} \cdot a^{n} = a^{m + n}

a ≠ 0

Quotient of powers

\frac{a^{m}}{a^{n}} = a^{m - n}

a ≠ 0

Power of a power

(a^{m})^{n} = a^{m n}

Power of a product

(a b)^{n} = a^{n} b^{n}

Power of a quotient

{(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}

b ≠ 0

Zero exponent

a^{0} = 1

a ≠ 0

Negative exponent

a^{- n} = \frac{1}{a^{n}}

a ≠ 0

Negative exponent of a fraction

{(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}

a ≠ 0, b ≠ 0

Fraction (rational) exponent

a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = {(\sqrt[n]{a})}^{m}

Negative base in parentheses

(- a)^{2} = (- a) (- a) = a^{2}

Negative sign outside the power

- a^{2} = - (a \cdot a)

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