Solve the following equation with a rational exponent: x23=64 .(1 point)
Responses
8
8
16
16
512
512
32
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.