Question
Solve the following equation with a rational exponent: 5x^4/3=80
.(1 point)
Responses
16
16
40.32
40.32
8
8
12
.(1 point)
Responses
16
16
40.32
40.32
8
8
12
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \):
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. Now, we will eliminate the rational exponent by raising both sides to the reciprocal of \(\frac{4}{3}\), which is \(\frac{3}{4}\):
\[
x = 16^{3/4}
\]
3. To compute \( 16^{3/4} \), we first find \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad \text{(since \( 16 = 2^4 \))}
\]
4. Now, raise \( 2 \) to the power of \( 3 \):
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[
\boxed{8}
\]
1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]
2. Now, we will eliminate the rational exponent by raising both sides to the reciprocal of \(\frac{4}{3}\), which is \(\frac{3}{4}\):
\[
x = 16^{3/4}
\]
3. To compute \( 16^{3/4} \), we first find \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad \text{(since \( 16 = 2^4 \))}
\]
4. Now, raise \( 2 \) to the power of \( 3 \):
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[
\boxed{8}
\]
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