Algebra Examples

${(\frac{5^{3}}{5^{4}})}^{- 3}$

Step 1

Cancel the common factor of $5^{3}$ and $5^{4}$ .

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Step 1.1

Multiply by $1$ .

${(\frac{5^{3} \cdot 1}{5^{4}})}^{- 3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5^{3}$ out of $5^{4}$ .

${(\frac{5^{3} \cdot 1}{5^{3} \cdot 5})}^{- 3}$

Step 1.2.2

Cancel the common factor.

${(\frac{5^{3} \cdot 1}{5^{3} \cdot 5})}^{- 3}$

Step 1.2.3

Rewrite the expression.

${(\frac{1}{5})}^{- 3}$

Step 2

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

$5^{3}$

Step 3

Raise $5$ to the power of $3$ .

$125$