Precalculus Examples

${(x^{- 5} y^{\frac{1}{4}})}^{- \frac{4}{5}}$

Step 1

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

${(\frac{1}{x^{5}} y^{\frac{1}{4}})}^{- \frac{4}{5}}$

Step 2

Combine $\frac{1}{x^{5}}$ and $y^{\frac{1}{4}}$ .

${(\frac{y^{\frac{1}{4}}}{x^{5}})}^{- \frac{4}{5}}$

Step 3

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

${(\frac{x^{5}}{y^{\frac{1}{4}}})}^{\frac{4}{5}}$

Step 4

Apply the product rule to $\frac{x^{5}}{y^{\frac{1}{4}}}$ .

$\frac{{(x^{5})}^{\frac{4}{5}}}{{(y^{\frac{1}{4}})}^{\frac{4}{5}}}$

Step 5

Multiply the exponents in ${(x^{5})}^{\frac{4}{5}}$ .

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Step 5.1

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

$\frac{x^{5 (\frac{4}{5})}}{{(y^{\frac{1}{4}})}^{\frac{4}{5}}}$

Step 5.2

Cancel the common factor of $5$ .

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Step 5.2.1

Cancel the common factor.

$\frac{x^{5 (\frac{4}{5})}}{{(y^{\frac{1}{4}})}^{\frac{4}{5}}}$

Step 5.2.2

Rewrite the expression.

$\frac{x^{4}}{{(y^{\frac{1}{4}})}^{\frac{4}{5}}}$

Step 6

Multiply the exponents in ${(y^{\frac{1}{4}})}^{\frac{4}{5}}$ .

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Step 6.1

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

$\frac{x^{4}}{y^{\frac{1}{4} \cdot \frac{4}{5}}}$

Step 6.2

Cancel the common factor of $4$ .

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Step 6.2.1

Cancel the common factor.

$\frac{x^{4}}{y^{\frac{1}{4} \cdot \frac{4}{5}}}$

Step 6.2.2

Rewrite the expression.

$\frac{x^{4}}{y^{\frac{1}{5}}}$