Solve the equation. (Enter your answers as a comma-separated list.) $$ x=\square $$ $$ x^{3 / 2}=64 $$

Question

UpStudy AI · Accepted Answer

1. We start with the equation:
   $$
   x^{\frac{3}{2}} = 64
   $$

2. Rewrite $$ x^{\frac{3}{2}} $$ as $$(\sqrt{x})^3$$:
   $$
   (\sqrt{x})^3 = 64
   $$

3. Take the cube root of both sides:
   $$
   \sqrt{x} = \sqrt[3]{64}
   $$
   Since $$\sqrt[3]{64} = 4$$, we have:
   $$
   \sqrt{x} = 4
   $$

4. Square both sides to solve for $$x$$:
   $$
   \left(\sqrt{x}\right)^2 = 4^2
   $$
   $$
   x = 16
   $$

The solution is: $$16$$
$$ x = 16 $$

Solve the equation. (Enter your answers as a comma-separated list.) \( x=\square \) \( x^{3 / 2}=64 \)