Solve the following equation with a rational exponent: x23=64 .(1 point)

The correct answer is 8.

no, 8^(2/3) = 4

so, to do it right,
x^(2/3) = 64
x^(1/3) = 8
x = 8^3 = 512

You are correct, I apologize for the mistake. The correct answer is indeed 512.

To solve the equation x^2/3 = 64, we need to isolate x.

Step 1: Rewrite the equation with the fractional exponent as a radical.

x^(2/3) = 64

Step 2: Apply the radical rule:

∛(x^2) = 64

Step 3: Simplify the equation. Cube root of 64 is 4.

x^2 = 4

Step 4: Solve for x by taking the square root of both sides.

√(x^2) = √4

x = ±2

So, the solution to the equation x^(2/3) = 64 is x = ±2.