# How do you simplify (3/5)^-2?

Sep 30, 2017

$\left(\frac{25}{9}\right) = 2 \left(\frac{7}{9}\right)$

#### Explanation:

${\left(\frac{3}{5}\right)}^{-} 2 = \frac{1}{\frac{3}{5}} ^ 2 = {\left(\frac{5}{3}\right)}^{2}$
$= {5}^{2} / {3}^{2} = \frac{5 \cdot 5}{3 \cdot 3}$
$= \frac{25}{9}$

Sep 30, 2017

The answer is $\frac{25}{9}$

#### Explanation:

Well the idea of a negative exponent is that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, if you were to have ${x}^{-} 3$, we would make it $\frac{1}{x} ^ 3$ So in this case, we have ${\left(\frac{3}{5}\right)}^{-} 2$ so it needs to be brought under the fraction line, making it $\frac{1}{\frac{3}{5}} ^ 2$ As you can see, the exponent becomes positive when you do this. From there, simply square the fraction $\frac{1}{\frac{9}{25}}$ and divide 1 by the fraction. As you probably know, dividing by a fraction flips it as well, so you have $1 \cdot \frac{25}{9}$ Which equals $\frac{25}{9}$ .