Question

For what value of a does 9 = (StartFraction 1 Over 27 EndFraction) Superscript a + 3?

Negative eleven-thirds
Negative seven-thirds
Seven-thirds
Eleven-thirds

Answer 1

A. -11/3

Explanation:

:)

Answer 2

`a=-(11)/(3)`

Explanation:

We want to find the value of
`a` for which
`9=((1)/(27))^(a+3)`.

We rewrite with a base of 3 to get:

`3^2=((1)/(3^3))^(a+3)`.

Recall that:
`(1)/(a^n)=a^(-n)`

`\implies 3^2=3^(-3(a+3))`.

We now equate the exponents to get:

`2=-3(a+3)`

`2=-3a-9`

`2+9=-3a`

`11=-3a`

`a=-(11)/(3)`

The first choice is correct