Basic Math Examples

${(a^{4} b^{- 8})}^{- \frac{1}{4}}$

Step 1

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

${(a^{4} \frac{1}{b^{8}})}^{- \frac{1}{4}}$

Step 2

Combine $a^{4}$ and $\frac{1}{b^{8}}$ .

${(\frac{a^{4}}{b^{8}})}^{- \frac{1}{4}}$

Step 3

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

${(\frac{b^{8}}{a^{4}})}^{\frac{1}{4}}$

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to $\frac{b^{8}}{a^{4}}$ .

$\frac{{(b^{8})}^{\frac{1}{4}}}{{(a^{4})}^{\frac{1}{4}}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{b^{8 (\frac{1}{4})}}{{(a^{4})}^{\frac{1}{4}}}$

Step 4.2.2

Cancel the common factor of $4$ .

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Step 4.2.2.1

Factor $4$ out of $8$ .

$\frac{b^{4 (2) \frac{1}{4}}}{{(a^{4})}^{\frac{1}{4}}}$

Step 4.2.2.2

Cancel the common factor.

$\frac{b^{4 \cdot 2 \frac{1}{4}}}{{(a^{4})}^{\frac{1}{4}}}$

Step 4.2.2.3

Rewrite the expression.

$\frac{b^{2}}{{(a^{4})}^{\frac{1}{4}}}$

Step 5

Simplify the denominator.

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Step 5.1

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

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Step 5.1.1

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

$\frac{b^{2}}{a^{4 (\frac{1}{4})}}$

Step 5.1.2

Cancel the common factor of $4$ .

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Step 5.1.2.1

Cancel the common factor.

$\frac{b^{2}}{a^{4 (\frac{1}{4})}}$

Step 5.1.2.2

Rewrite the expression.

$\frac{b^{2}}{a^{1}}$

Step 5.2

Simplify.

$\frac{b^{2}}{a}$