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