Algebra Examples

${(\frac{m^{13}}{m^{20}})}^{- 3}$

Step 1

Cancel the common factor of $m^{13}$ and $m^{20}$ .

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Step 1.1

Multiply by $1$ .

${(\frac{m^{13} \cdot 1}{m^{20}})}^{- 3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $m^{13}$ out of $m^{20}$ .

${(\frac{m^{13} \cdot 1}{m^{13} m^{7}})}^{- 3}$

Step 1.2.2

Cancel the common factor.

${(\frac{m^{13} \cdot 1}{m^{13} m^{7}})}^{- 3}$

Step 1.2.3

Rewrite the expression.

${(\frac{1}{m^{7}})}^{- 3}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(m^{7})}^{3}$

Step 3

Multiply the exponents in ${(m^{7})}^{3}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$m^{7 \cdot 3}$

Step 3.2

Multiply $7$ by $3$ .

$m^{21}$