Basic Math Examples

${(64 y^{3})}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(64 y^{3})}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $64 y^{3}$ .

$\frac{1}{64^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}}$

Step 2.2

Rewrite $64$ as $4^{3}$ .

$\frac{1}{{(4^{3})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}}$

Step 2.3

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

$\frac{1}{4^{3 (\frac{1}{3})} {(y^{3})}^{\frac{1}{3}}}$

Step 2.4

Cancel the common factor of $3$ .

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Step 2.4.1

Cancel the common factor.

$\frac{1}{4^{3 (\frac{1}{3})} {(y^{3})}^{\frac{1}{3}}}$

Step 2.4.2

Rewrite the expression.

$\frac{1}{4^{1} {(y^{3})}^{\frac{1}{3}}}$

Step 2.5

Evaluate the exponent.

$\frac{1}{4 {(y^{3})}^{\frac{1}{3}}}$

Step 2.6

Multiply the exponents in ${(y^{3})}^{\frac{1}{3}}$ .

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Step 2.6.1

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

$\frac{1}{4 y^{3 (\frac{1}{3})}}$

Step 2.6.2

Cancel the common factor of $3$ .

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Step 2.6.2.1

Cancel the common factor.

$\frac{1}{4 y^{3 (\frac{1}{3})}}$

Step 2.6.2.2

Rewrite the expression.

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

Step 2.7

Simplify.

$\frac{1}{4 y}$