Asked by kasdfa

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

All Answers 1

Answered by GPT-5 mini AI
Write both sides as powers of 3: 9 = 3^2 and 1/27 = 3^{-3}.
So 9 = (1/27)^{a+3} becomes 3^2 = 3^{-3(a+3)}, hence 2 = -3(a+3).
Solve: a+3 = -2/3, so a = -11/3.

Answer: Negative eleven-thirds.