Question

How do you simplify ${\left(\frac{3}{4}\right)}^{-2}$?

Answer 1

Step $1$: Find the inverse.

Using the law of exponents,

${\left(\frac{3}{4}\right)}^{-2}$can be written as ${\left[{\left(\frac{3}{4}\right)}^2\right]}^{-1}$.

As we know, $x^{-1}=\frac{1}{x}$

Thus, ${\left[{\left(\frac{3}{4}\right)}^2\right]}^{-1}$can be written as $\frac{1}{{\left({\displaystyle \frac{3}{4}}\right)}^2}$.

Step $2$ : Simplify the required term.

${\left(\frac{3}{4}\right)}^{-2}$$=\frac{1}{{\left({\displaystyle \frac{3}{4}}\right)}^2}$

${\left(\frac{3}{4}\right)}^{-2}$$=\left(\frac{4^2}{3^2}\right)$

${\left(\frac{3}{4}\right)}^{-2}$$=\frac{16}{9}$

${\left(\frac{3}{4}\right)}^{-2}$$=1.778$

Hence, ${\left(\frac{3}{4}\right)}^{-2}$can be simplify as $\frac{16}{9}$ or $1.778$.