Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $4$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

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

Step 2.5

Evaluate the exponent.

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

Step 2.6

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

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Step 2.6.1

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

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

Step 2.6.2

Cancel the common factor of $4$ .

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Step 2.6.2.1

Factor $4$ out of $8$ .

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

Step 2.6.2.2

Cancel the common factor.

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

Step 2.6.2.3

Rewrite the expression.

$\frac{1}{2 y^{2}}$