Algebra Examples

${(\frac{16}{81 y^{4}})}^{- \frac{3}{4}}$

Step 1

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

${(\frac{81 y^{4}}{16})}^{\frac{3}{4}}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{81 y^{4}}{16}$ .

$\frac{{(81 y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 2.2

Apply the product rule to $81 y^{4}$ .

$\frac{81^{\frac{3}{4}} {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $81$ as $3^{4}$ .

$\frac{{(3^{4})}^{\frac{3}{4}} {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3.2

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

$\frac{3^{4 (\frac{3}{4})} {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3^{4 (\frac{3}{4})} {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3.3.2

Rewrite the expression.

$\frac{3^{3} {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3.4

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

$\frac{27 {(y^{4})}^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

Step 3.5

Multiply the exponents in ${(y^{4})}^{\frac{3}{4}}$ .

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Step 3.5.1

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

$\frac{27 y^{4 (\frac{3}{4})}}{16^{\frac{3}{4}}}$

Step 3.5.2

Cancel the common factor of $4$ .

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Step 3.5.2.1

Cancel the common factor.

$\frac{27 y^{4 (\frac{3}{4})}}{16^{\frac{3}{4}}}$

Step 3.5.2.2

Rewrite the expression.

$\frac{27 y^{3}}{16^{\frac{3}{4}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $16$ as $2^{4}$ .

$\frac{27 y^{3}}{{(2^{4})}^{\frac{3}{4}}}$

Step 4.2

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

$\frac{27 y^{3}}{2^{4 (\frac{3}{4})}}$

Step 4.3

Cancel the common factor of $4$ .

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Step 4.3.1

Cancel the common factor.

$\frac{27 y^{3}}{2^{4 (\frac{3}{4})}}$

Step 4.3.2

Rewrite the expression.

$\frac{27 y^{3}}{2^{3}}$

Step 4.4

Raise $2$ to the power of $3$ .

$\frac{27 y^{3}}{8}$