Evaluate (1/16)^(3/4)

${(\frac{1}{16})}^{\frac{3}{4}}$

Step 1

Simplify the expression.

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

$\frac{1^{\frac{3}{4}}}{16^{\frac{3}{4}}}$

One to any power is one.

$\frac{1}{16^{\frac{3}{4}}}$

Step 2

Simplify the denominator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{1}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$