Question

Solve the following equation with a rational exponent:  5x4/3=80 .(1 point)Responses40.3240.3288161612

Answer 1

To solve the equation \( 5x^{4/3} = 80 \), we can start by isolating \( x^{4/3} \).

1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]

2. Next, we need to eliminate the exponent \( \frac{4}{3} \). To do this, we can raise both sides of the equation to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{\frac{3}{4}}
\]

3. Now, we can simplify \( 16^{\frac{3}{4}} \):
- First, find \( 16^{\frac{1}{4}} \), which is the fourth root of 16:
\[
16^{\frac{1}{4}} = 2
\]
- Now raise this result to the power of 3:
\[
x = 2^3 = 8
\]

Thus, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[
\boxed{8}
\]

Note: Since the provided responses don’t include 8, please double-check the options given.