Questions: Solve the equation. x^(3 / 2) = 64 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The solution set is . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution set is the empty set.

Solution Steps

To solve the equation \( x^{3/2} = 64 \), we need to isolate \( x \). We can do this by raising both sides of the equation to the power of \( \frac{2}{3} \), which is the reciprocal of \( \frac{3}{2} \). This will give us \( x \) on one side of the equation.

To solve the equation \( x^{3/2} = 64 \), we need to isolate \( x \). We can do this by raising both sides of the equation to the power of \( \frac{2}{3} \), which is the reciprocal of \( \frac{3}{2} \).

Raise both sides of the equation to the power of \( \frac{2}{3} \): \[ (x^{3/2})^{2/3} = 64^{2/3} \]

The left side simplifies to: \[ x = 64^{2/3} \]

Calculate \( 64^{2/3} \): \[ 64^{2/3} = 16 \]

Final Answer