# What is 4s over 3t to the negative 2nd power times 2s over 6t to the 2nd power? The format is a bit weird .

## ${\left(\frac{4 s}{3 t}\right)}^{- 2} \times {\left(\frac{2 s}{6 t}\right)}^{2}$

Apr 18, 2018

$\frac{1}{16}$

#### Explanation:

${\left(\frac{4 s}{3 t}\right)}^{- 2} \cdot {\left(\frac{2 s}{6 t}\right)}^{2}$

First when given a negative exponent, I reciprocate the expression and make the exponent positive, so:

${\left(\frac{3 t}{4 s}\right)}^{2} \cdot {\left(\frac{2 s}{6 t}\right)}^{2}$

${\left(3 t\right)}^{2} / {\left(4 s\right)}^{2} \cdot {\left(2 s\right)}^{2} / {\left(6 t\right)}^{2}$

$\frac{\left(3 t\right) \left(3 t\right)}{\left(4 s\right) \left(4 s\right)} \cdot \frac{\left(2 s\right) \left(2 s\right)}{\left(6 t\right) \left(6 t\right)}$

$\frac{9 {t}^{2}}{16 {s}^{2}} \cdot \frac{4 {s}^{2}}{36 {t}^{2}}$

Cross simplify:

$\frac{\cancel{9 {t}^{2}}}{\cancel{16 {s}^{2}} 4} \cdot \frac{\cancel{4 {s}^{2}}}{\cancel{36 {t}^{2}} 4} =$

$\frac{1}{16}$