Solve the following equation with a rational exponent: X 2/3=64.(1 point)

Question

Responses

16
16

8
8

32
32

512
512

Answer 1

To solve the equation \( X^{\frac{2}{3}} = 64 \), we can start by raising both sides of the equation to the reciprocal of the exponent, which is \( \frac{3}{2} \).

\[ X = 64^{\frac{3}{2}} \]

Now we can simplify \( 64^{\frac{3}{2}} \):

1. First, find the square root of 64: \[ \sqrt{64} = 8 \]

2. Then raise it to the power of 3: \[ 8^3 = 512 \]

Thus, we have: \[ X = 512 \]

So the solution to the equation \( X^{\frac{2}{3}} = 64 \) is:

\(\boxed{512}\)