Question

Evaluate 3^x for x = −2, x = 1, and x = 3.

Answer 1

We need to evaluate the exponential function for some values of x.

First, remember that:

$3^x=3\cdot3\cdot3\cdot3\ldots\cdot3\text{ (x factors)}$

For example:

$3^2=3\cdot3\text{ (two factors)}$

Also, the negative exponent inverts the base:

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

So, for x = -2, we have:

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

For x = 1, we have:

$3^1=3$

For x = 3, we have:

$3^3=3\cdot3\cdot3=27$

Therefore, the answer is:

1/9, 3, 27