Solve the following equation with a rational exponent:  x2/3=64 .(1 point)Responses323216165125128

To solve the equation \( x^{2/3} = 64 \), follow these steps:

1. Raise both sides to the reciprocal of the exponent \( \frac{3}{2} \):

\[ (x^{2/3})^{3/2} = 64^{3/2} \]

2. Simplifying the left side:

\[ x^{(2/3) \cdot (3/2)} = x^1 = x \]

3. Now compute the right side:

First, calculate \( 64^{3/2} \):

• Calculate \( 64^{1/2} = \sqrt{64} = 8 \).
• Then raise the result to the third power: \( 8^3 = 512 \).

So:

\[ x = 512 \]

Thus, the value of \( x \) is \( 512 \).

Therefore, the answer is \( 512 \).