# How do you simplify 2^2/(3/2)^-2?

Sep 17, 2015

9

#### Explanation:

Make that negative power into a multiplication, since dividing a negative power just makes it positive

${2}^{2} \cdot {\left(\frac{3}{2}\right)}^{2}$

Expand the power to both numerator and denominator

${2}^{2} \cdot \frac{3}{2} \cdot \frac{3}{2} = {2}^{2} \cdot {3}^{2} / {2}^{2}$

The ${2}^{2}$ on the numerator cancels the one in the denominator,

${2}^{2} \cdot {3}^{2} / {2}^{2} = {3}^{2}$

Evaluate that

${3}^{2} = 3 \cdot 3 = 9$