Evaluate (1/4)^(5/2)

${(\frac{1}{4})}^{\frac{5}{2}}$

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{4}$ .

$\frac{1^{\frac{5}{2}}}{4^{\frac{5}{2}}}$

One to any power is one.

$\frac{1}{4^{\frac{5}{2}}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(2^{2})}^{\frac{5}{2}}}$

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

$\frac{1}{2^{2 (\frac{5}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2^{2 (\frac{5}{2})}}$

Rewrite the expression.

$\frac{1}{2^{5}}$

Raise $2$ to the power of $5$ .

$\frac{1}{32}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{32}$

Decimal Form:

$0.03125$