Simplify (27/8)^(-2/3)

${(\frac{27}{8})}^{- \frac{2}{3}}$

Step 1

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

${(\frac{8}{27})}^{\frac{2}{3}}$

Step 2

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

$\frac{8^{\frac{2}{3}}}{27^{\frac{2}{3}}}$

Step 3

Simplify the numerator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $3$ to the power of $2$ .

$\frac{4}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$