Asked by .
Solve the following equation with a rational exponent: 5x43=80
.(1 point)
Responses
8
8
12
12
16
16
40.32
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equation as 5x^(4/3) = 80.
Divide by 5: x^(4/3) = 16.
Raise both sides to the 3/4 power: x = 16^(3/4) = (2^4)^(3/4) = 2^3 = 8.
(If you solve via t = x^(1/3), then t^4 = 16 gives t = ±2 and x = t^3 = ±8, so x = −8 also satisfies the original equation. The multiple‑choice answer is 8.)
Divide by 5: x^(4/3) = 16.
Raise both sides to the 3/4 power: x = 16^(3/4) = (2^4)^(3/4) = 2^3 = 8.
(If you solve via t = x^(1/3), then t^4 = 16 gives t = ±2 and x = t^3 = ±8, so x = −8 also satisfies the original equation. The multiple‑choice answer is 8.)
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