Algebra Examples

${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 2}$

Step 1

Multiply the exponents in ${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 2}$ .

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Step 1.1

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

${(\frac{1}{64})}^{\frac{1}{3} \cdot - 2}$

Step 1.2

Combine $\frac{1}{3}$ and $- 2$ .

${(\frac{1}{64})}^{\frac{- 2}{3}}$

Step 1.3

Move the negative in front of the fraction.

${(\frac{1}{64})}^{- \frac{2}{3}}$

Step 2

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

$64^{\frac{2}{3}}$

Step 3

Simplify the expression.

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Step 3.1

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

${(4^{3})}^{\frac{2}{3}}$

Step 3.2

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

$4^{3 (\frac{2}{3})}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$4^{3 (\frac{2}{3})}$

Step 4.2

Rewrite the expression.

$4^{2}$

Step 5

Raise $4$ to the power of $2$ .

$16$