Evaluate (1/16)^(3/2)

${(\frac{1}{16})}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{16}$ .

$\frac{1^{\frac{3}{2}}}{16^{\frac{3}{2}}}$

One to any power is one.

$\frac{1}{16^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{1}{{(4^{2})}^{\frac{3}{2}}}$

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

$\frac{1}{4^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{4^{2 (\frac{3}{2})}}$

Rewrite the expression.

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

Raise $4$ to the power of $3$ .

$\frac{1}{64}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64}$

Decimal Form:

$0.015625$