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 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 5

Multiply the exponents in

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

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

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Step 5.1

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 5.2

Cancel the common factor of

3

$3$ .

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Step 5.2.1

Cancel the common factor.

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

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

Step 5.2.2

Rewrite the expression.

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

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

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

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

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

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

Step 6

Simplify the denominator.

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Step 6.1

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

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

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

Step 6.2

Apply the power rule and multiply exponents,

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

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

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

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

Step 6.3

Cancel the common factor of

3

$3$ .

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Step 6.3.1

Cancel the common factor.

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

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

Step 6.3.2

Rewrite the expression.

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

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

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

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

Step 6.4

Raise

2

$2$ to the power of

2

$2$ .

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

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

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

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$