1Cademy - Simplifying $$\left(\frac{k}{j}\right)^{-3}$$ and $$\left(\frac{m}{n}\right)^{-7}$$ by Distributing a Negative Exponent

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Simplifying $\left(\frac{3}{7}\right)^2$ , $\left(\frac{b}{3}\right)^4$ , and $\left(\frac{k}{j}\right)^3$ Using the Quotient to a Power Property

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Simplifying $\left(\frac{k}{j}\right)^{-3}$ and $\left(\frac{m}{n}\right)^{-7}$ by Distributing a Negative Exponent

Simplify a fraction raised to a negative power by distributing the exponent and applying the definition of a negative exponent.

ⓐ $\left(\frac{k}{j}\right)^{-3} = \frac{j^3}{k^3}$ : First, raise both the numerator and denominator to the power $-3$ using the Quotient to a Power Property: $\frac{k^{-3}}{j^{-3}}$ . Next, apply the definition of a negative exponent ( $a^{-n} = \frac{1}{a^n}$ ) to rewrite the expression with positive exponents. Moving $k^{-3}$ to the denominator as $k^3$ and $j^{-3}$ to the numerator as $j^3$ yields $\frac{j^3}{k^3}$ .

ⓑ $\left(\frac{m}{n}\right)^{-7} = \frac{n^7}{m^7}$ : Raise both the numerator and denominator to the power $-7$ : $\frac{m^{-7}}{n^{-7}}$ . Use the definition of a negative exponent to rewrite the expression with positive exponents, which flips the positions to get $\frac{n^7}{m^7}$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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