Algebra Examples

${(16 x^{8} y^{- 4})}^{- \frac{1}{4}}$

Step 1

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

${(16 x^{8} \frac{1}{y^{4}})}^{- \frac{1}{4}}$

Step 2

Multiply $16 x^{8} \frac{1}{y^{4}}$ .

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Step 2.1

Combine $16$ and $\frac{1}{y^{4}}$ .

${(x^{8} \frac{16}{y^{4}})}^{- \frac{1}{4}}$

Step 2.2

Combine $x^{8}$ and $\frac{16}{y^{4}}$ .

${(\frac{x^{8} \cdot 16}{y^{4}})}^{- \frac{1}{4}}$

Step 3

Move $16$ to the left of $x^{8}$ .

${(\frac{16 \cdot x^{8}}{y^{4}})}^{- \frac{1}{4}}$

Step 4

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

${(\frac{y^{4}}{16 x^{8}})}^{\frac{1}{4}}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{y^{4}}{16 x^{8}}$ .

$\frac{{(y^{4})}^{\frac{1}{4}}}{{(16 x^{8})}^{\frac{1}{4}}}$

Step 5.2

Apply the product rule to $16 x^{8}$ .

$\frac{{(y^{4})}^{\frac{1}{4}}}{16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 6

Simplify the numerator.

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Step 6.1

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

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Step 6.1.1

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

$\frac{y^{4 (\frac{1}{4})}}{16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 6.1.2

Cancel the common factor of $4$ .

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Step 6.1.2.1

Cancel the common factor.

$\frac{y^{4 (\frac{1}{4})}}{16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 6.1.2.2

Rewrite the expression.

$\frac{y^{1}}{16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 6.2

Simplify.

$\frac{y}{16^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 7

Simplify the denominator.

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Step 7.1

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

$\frac{y}{{(2^{4})}^{\frac{1}{4}} {(x^{8})}^{\frac{1}{4}}}$

Step 7.2

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

$\frac{y}{2^{4 (\frac{1}{4})} {(x^{8})}^{\frac{1}{4}}}$

Step 7.3

Cancel the common factor of $4$ .

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Step 7.3.1

Cancel the common factor.

$\frac{y}{2^{4 (\frac{1}{4})} {(x^{8})}^{\frac{1}{4}}}$

Step 7.3.2

Rewrite the expression.

$\frac{y}{2^{1} {(x^{8})}^{\frac{1}{4}}}$

Step 7.4

Evaluate the exponent.

$\frac{y}{2 {(x^{8})}^{\frac{1}{4}}}$

Step 7.5

Multiply the exponents in ${(x^{8})}^{\frac{1}{4}}$ .

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Step 7.5.1

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

$\frac{y}{2 x^{8 (\frac{1}{4})}}$

Step 7.5.2

Cancel the common factor of $4$ .

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Step 7.5.2.1

Factor $4$ out of $8$ .

$\frac{y}{2 x^{4 (2) \frac{1}{4}}}$

Step 7.5.2.2

Cancel the common factor.

$\frac{y}{2 x^{4 \cdot 2 \frac{1}{4}}}$

Step 7.5.2.3

Rewrite the expression.

$\frac{y}{2 x^{2}}$