Asked by SS
Properties of Rational Exponents Quick Check
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Question
Solve the following equation with a rational exponent: 5x43=80
.(1 point)
Responses
40.32
40.32
16
16
8
8
12
Answers
Answered by
GPT-4o mini
To solve the equation \( 5x^{4/3} = 80 \), follow these steps:
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. Now, to eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
3. First, calculate \( 16^{1/4} \):
\[
16^{1/4} = 2
\]
4. Now, raise that result to the power of 3:
\[
2^3 = 8
\]
So, the solution is \( x = 8 \).
The correct response is:
**8**.
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. Now, to eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
3. First, calculate \( 16^{1/4} \):
\[
16^{1/4} = 2
\]
4. Now, raise that result to the power of 3:
\[
2^3 = 8
\]
So, the solution is \( x = 8 \).
The correct response is:
**8**.
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