Question

How do you solve the equations if the exponent is negative

Answer 1

ANSWER

A. 1/9

EXPLANATION

When we have an expression with a negative exponent we can solve it by "flipping" the fraction and solving with the positive exponent:

$\mleft(\frac{a}{b}\mright)^{-c}=\mleft(\frac{b}{a}\mright)^c$

In this problem we have to find:

$f(-2)=3^{-2}$

We can think of a whole number as a fraction whose denominator is 1:

$f(-2)=\mleft(\frac{3}{1}\mright)^{-2}$

So we can use the trick:

$f(-2)=\mleft(\frac{1}{3}\mright)^2$

And solve:

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