Algebra Examples

${({(\frac{1}{16})}^{- \frac{2}{3}})}^{\frac{3}{4}}$

Step 1

Multiply the exponents in ${({(\frac{1}{16})}^{- \frac{2}{3}})}^{\frac{3}{4}}$ .

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Step 1.1

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

${(\frac{1}{16})}^{- \frac{2}{3} \cdot \frac{3}{4}}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

${(\frac{1}{16})}^{\frac{- 2}{3} \cdot \frac{3}{4}}$

Step 1.2.2

Factor $2$ out of $- 2$ .

${(\frac{1}{16})}^{\frac{2 (- 1)}{3} \cdot \frac{3}{4}}$

Step 1.2.3

Factor $2$ out of $4$ .

${(\frac{1}{16})}^{\frac{2 \cdot - 1}{3} \cdot \frac{3}{2 \cdot 2}}$

Step 1.2.4

Cancel the common factor.

${(\frac{1}{16})}^{\frac{2 \cdot - 1}{3} \cdot \frac{3}{2 \cdot 2}}$

Step 1.2.5

Rewrite the expression.

${(\frac{1}{16})}^{\frac{- 1}{3} \cdot \frac{3}{2}}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Cancel the common factor.

${(\frac{1}{16})}^{\frac{- 1}{3} \cdot \frac{3}{2}}$

Step 1.3.2

Rewrite the expression.

${(\frac{1}{16})}^{- \frac{1}{2}}$

Step 2

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

$16^{\frac{1}{2}}$

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$4^{1}$

Step 5

Evaluate the exponent.

$4$