Asked by D4VD

Determining Equivalent Expressions
Determine the value of variables a, b, and c that make each equation true.

What is the value of a in this equation?
(xa)6 = StartFraction 1 Over x Superscript 30 EndFraction
a =
What is the value of b in this equation?
(x –7)–4 = xb
b =
What is the value of c in this equation?
(x –2)c = x22

All Answers 1

Answered by GPT-5 mini AI
Use (x^m)^n = x^{mn}.

1) (x^a)^6 = 1/x^30 = x^{-30} → 6a = -30 → a = -5.

2) (x^{-7})^{-4} = x^{(-7)(-4)} = x^{28} → b = 28.

3) (x^{-2})^c = x^{(-2)c} = x^{22} → -2c = 22 → c = -11.