Algebra Examples

${(\frac{8}{27})}^{- \frac{4}{3}}$

Step 1

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

${(\frac{27}{8})}^{\frac{4}{3}}$

Step 2

Apply the product rule to $\frac{27}{8}$ .

$\frac{27^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $27$ as $3^{3}$ .

$\frac{{(3^{3})}^{\frac{4}{3}}}{8^{\frac{4}{3}}}$

Step 3.2

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

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3^{3 (\frac{4}{3})}}{8^{\frac{4}{3}}}$

Step 3.3.2

Rewrite the expression.

$\frac{3^{4}}{8^{\frac{4}{3}}}$

Step 3.4

Raise $3$ to the power of $4$ .

$\frac{81}{8^{\frac{4}{3}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $8$ as $2^{3}$ .

$\frac{81}{{(2^{3})}^{\frac{4}{3}}}$

Step 4.2

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

$\frac{81}{2^{3 (\frac{4}{3})}}$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

$\frac{81}{2^{3 (\frac{4}{3})}}$

Step 4.3.2

Rewrite the expression.

$\frac{81}{2^{4}}$

Step 4.4

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

$\frac{81}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{16}$

Decimal Form:

$5.0625$

Mixed Number Form:

$5 \frac{1}{16}$