What is the value of (3/4)^-2

Question

16/9

-9/16

9/16

-16/9

Answer 1

To evaluate $(\frac{3}{4}{)}^{-2}$, we can use the property of exponents that states $a^{-n}=\frac{1}{a^n}$. Therefore:

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

Next, we calculate $(\frac{3}{4}{)}^2$:

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

Now we plug this back into our expression:

$$(\frac{3}{4}{)}^{-2}=\frac{1}{\frac{9}{16}}=\frac{16}{9}$$

Thus, the value of $(\frac{3}{4}{)}^{-2}$ is:

$$\boxed{{\displaystyle \frac{16}{9}}}$$