Properties of Rational Exponents Quick Check

Question

4 of 54 of 5 Items
Question
Solve the following equation with a rational exponent: 5x43=80
.(1 point)
Responses

40.32
40.32

16
16

8
8

12

Answer 1

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.