Evaluate 1/3(27)^(-2/3)

$\frac{1}{3} {(27)}^{- \frac{2}{3}}$

Step 1

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

$\frac{1}{3} \cdot \frac{1}{27^{\frac{2}{3}}}$

Step 2

Combine fractions.

Combine.

$\frac{1 \cdot 1}{3 \cdot 27^{\frac{2}{3}}}$

Multiply $1$ by $1$ .

$\frac{1}{3 \cdot 27^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

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

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

Multiply the exponents in ${(3^{3})}^{\frac{2}{3}}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

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

Step 4

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

$\frac{1}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{27}$

Decimal Form:

$0.\overline{037}$