Evaluate (27/8)^(-4/3)

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

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

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

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

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

Simplify the numerator.

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

$\frac{{(2^{3})}^{\frac{4}{3}}}{27^{\frac{4}{3}}}$

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

$\frac{2^{3 (\frac{4}{3})}}{27^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{2^{3 (\frac{4}{3})}}{27^{\frac{4}{3}}}$

Rewrite the expression.

$\frac{2^{4}}{27^{\frac{4}{3}}}$

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

$\frac{16}{27^{\frac{4}{3}}}$

Simplify the denominator.

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

$\frac{16}{{(3^{3})}^{\frac{4}{3}}}$

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

$\frac{16}{3^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{16}{3^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{16}{3^{4}}$

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

$\frac{16}{81}$

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{81}$

Decimal Form:

$0.19753086 \dots$

Evaluate (27/8)^(-4/3)

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