Evaluate 1/3(8)^(-2/3)

$\frac{1}{3} {(8)}^{- \frac{2}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3} \cdot \frac{1}{8^{\frac{2}{3}}}$

Step 2

Combine fractions.

Combine.

$\frac{1 \cdot 1}{3 \cdot 8^{\frac{2}{3}}}$

Multiply $1$ by $1$ .

$\frac{1}{3 \cdot 8^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{1}{3 \cdot 4}$

Step 4

Multiply $3$ by $4$ .

$\frac{1}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{12}$

Decimal Form:

$0.08\overline{3}$