Precalculus Examples

$32^{25^{- 8^{- 3^{- 1}}}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$32^{25^{- 8^{- \frac{1}{3}}}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$32^{25^{- \frac{1}{8^{\frac{1}{3}}}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $8$ as $2^{3}$ .

$32^{25^{- \frac{1}{{(2^{3})}^{\frac{1}{3}}}}}$

Step 3.2

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

$32^{25^{- \frac{1}{2^{3 (\frac{1}{3})}}}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

$32^{25^{- \frac{1}{2^{3 (\frac{1}{3})}}}}$

Step 3.3.2

Rewrite the expression.

$32^{25^{- \frac{1}{2^{1}}}}$

Step 3.4

Evaluate the exponent.

$32^{25^{- \frac{1}{2}}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$32^{\frac{1}{25^{\frac{1}{2}}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $25$ as $5^{2}$ .

$32^{\frac{1}{{(5^{2})}^{\frac{1}{2}}}}$

Step 5.2

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

$32^{\frac{1}{5^{2 (\frac{1}{2})}}}$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Cancel the common factor.

$32^{\frac{1}{5^{2 (\frac{1}{2})}}}$

Step 5.3.2

Rewrite the expression.

$32^{\frac{1}{5^{1}}}$

Step 5.4

Evaluate the exponent.

$32^{\frac{1}{5}}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Rewrite $32$ as $2^{5}$ .

${(2^{5})}^{\frac{1}{5}}$

Step 6.2

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

$2^{5 (\frac{1}{5})}$

Step 6.3

Cancel the common factor of $5$ .

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Step 6.3.1

Cancel the common factor.

$2^{5 (\frac{1}{5})}$

Step 6.3.2

Rewrite the expression.

$2^{1}$

Step 7

Evaluate the exponent.

$2$