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)=((1)/(3))^a`

So, for x = -2, we have:

`3^(-2)=((1)/(3))^2=(1)/(3)\cdot(1)/(3)=(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