Algebra Examples

{(8 a^{- 3})}^{- \frac{2}{3}}

${(8 a^{- 3})}^{- \frac{2}{3}}$

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

{(8 \frac{1}{a^{3}})}^{- \frac{2}{3}}

${(8 \frac{1}{a^{3}})}^{- \frac{2}{3}}$

Step 2

Combine

8

$8$ and

\frac{1}{a^{3}}

$\frac{1}{a^{3}}$ .

{(\frac{8}{a^{3}})}^{- \frac{2}{3}}

${(\frac{8}{a^{3}})}^{- \frac{2}{3}}$

Step 3

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

{(\frac{a^{3}}{8})}^{\frac{2}{3}}

${(\frac{a^{3}}{8})}^{\frac{2}{3}}$

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to

\frac{a^{3}}{8}

$\frac{a^{3}}{8}$ .

\frac{{(a^{3})}^{\frac{2}{3}}}{8^{\frac{2}{3}}}

$\frac{{(a^{3})}^{\frac{2}{3}}}{8^{\frac{2}{3}}}$

Step 4.2

Multiply the exponents in

{(a^{3})}^{\frac{2}{3}}

${(a^{3})}^{\frac{2}{3}}$ .

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Step 4.2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{a^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}}

$\frac{a^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}}$

Step 4.2.2

Cancel the common factor of

3

$3$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{a^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}}$

Step 4.2.2.2

Rewrite the expression.

$\frac{a^{2}}{8^{\frac{2}{3}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite

$8$ as

$2^{3}$ .

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

Step 5.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 5.3

Cancel the common factor of

$3$ .

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Step 5.3.1

Cancel the common factor.

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

Step 5.3.2

Rewrite the expression.

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

Step 5.4

Raise

$2$ to the power of

$2$ .

$\frac{a^{2}}{4}$