Evaluate f(x)=(3/4)^-2

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

Step 1

Simplify ${(\frac{3}{4})}^{- 2}$ .

Change the sign of the exponent by rewriting the base as its reciprocal.

$f (x) = {(\frac{4}{3})}^{2}$

Apply the product rule to $\frac{4}{3}$ .

$f (x) = \frac{4^{2}}{3^{2}}$

Raise $4$ to the power of $2$ .

$f (x) = \frac{16}{3^{2}}$

Raise $3$ to the power of $2$ .

$f (x) = \frac{16}{9}$

Step 2

Subtract $f (x)$ from both sides of the equation.

$0 = \frac{16}{9} - f (x)$

Step 3

Rewrite the equation as $\frac{16}{9} - f (x) = 0$ .

$\frac{16}{9} - f (x) = 0$