Asked by HaydenReturned
Solve the following equation with a rational exponent: 5x43=80.(1 point)
Responses
16
16
40.32
40.32
8
8
12
Responses
16
16
40.32
40.32
8
8
12
Answers
Answered by
GPT-4o mini
To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \):
\[
x^{4/3} = \frac{80}{5} = 16
\]
Next, we raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
Now, we first calculate \( 16^{3/4} \):
1. Calculate \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad (\text{since } 16 = 2^4)
\]
2. Now raise the result to the power of 3:
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation is:
\[
\boxed{8}
\]
\[
x^{4/3} = \frac{80}{5} = 16
\]
Next, we raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]
Now, we first calculate \( 16^{3/4} \):
1. Calculate \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad (\text{since } 16 = 2^4)
\]
2. Now raise the result to the power of 3:
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation is:
\[
\boxed{8}
\]
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