Solve the following equation with a rational exponent: 5x43=80

.(1 point)
Responses

16
16

8
8

12
12

40.32

1 answer

To solve the equation \( 5x^{4/3} = 80 \), we'll first isolate the \( x^{4/3} \) term.

  1. Divide both sides by 5:

\[ x^{4/3} = \frac{80}{5} = 16 \]

  1. Now we will eliminate the exponent by raising both sides to the reciprocal of the exponent \( \frac{3}{4} \):

\[ x = 16^{\frac{3}{4}} \]

  1. We can simplify \( 16^{\frac{3}{4}} \):

    • First, we find \( 16^{\frac{1}{4}} \): \[ 16^{\frac{1}{4}} = 2 \] because \( 2^4 = 16 \).

    • Now raise this result to the power of 3: \[ 16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8 \]

So, the solution to the equation \( 5x^{4/3} = 80 \) is:

\[ \boxed{8} \]

Thus, the correct response is 8.