Algebra Examples

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

Step 1

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 4

Simplify.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor of $4$ .

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Step 5.2.1

Factor $4$ out of $8$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$x y^{2}$