Simplify (8/27)^(-1/3)

${(\frac{8}{27})}^{\frac{- 1}{3}}$

Move the negative in front of the fraction.

${(\frac{8}{27})}^{- \frac{1}{3}}$

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

${(\frac{27}{8})}^{\frac{1}{3}}$

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

$\frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Simplify the numerator.

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

$\frac{{(3^{3})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

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

$\frac{3^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{3^{1}}{8^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{3}{8^{\frac{1}{3}}}$

Simplify the denominator.

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

$\frac{3}{{(2^{3})}^{\frac{1}{3}}}$

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

$\frac{3}{2^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{3}{2^{1}}$

Evaluate the exponent.

$\frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$