Evaluate (1/9)^(3/2)

${(\frac{1}{9})}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{9}$ .

$\frac{1^{\frac{3}{2}}}{9^{\frac{3}{2}}}$

One to any power is one.

$\frac{1}{9^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{1}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{27}$

Decimal Form:

$0.\overline{037}$