Simplify (2^-2)^(3/2)

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

Step 1

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2^{- 1 \cdot 3}$

Multiply $- 1$ by $3$ .

$2^{- 3}$

Step 2

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

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

Step 3

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

$\frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$