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

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the numerator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{9}{8^{\frac{2}{3}}}$

Step 4

Simplify the denominator.

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

$\frac{9}{{(2^{3})}^{\frac{2}{3}}}$

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

$\frac{9}{2^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{9}{2^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{9}{2^{2}}$

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

$\frac{9}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$