Rewrite the exponential expression as a radical expression: $-3x^{2/3}$

Expert intro: This is a power-to-radical conversion problem. Use the rule $a^{m/n}=\sqrt[n]{a^m}$ and keep the coefficient outside the radical.

Detailed walkthrough

We rewrite the fractional exponent using the radical rule:

$x^{2/3}=\sqrt[3]{x^2}$

Then multiply by the coefficient $-3$:

$-3x^{2/3}=-3\sqrt[3]{x^2}$

So the radical form is:

$\boxed{-3\sqrt[3]{x^2}}$

💡 Pitfall guide

A common mistake is putting the coefficient inside the radical as $\sqrt[3]{-3x^2}$. That changes the value, because the $-3$ is a separate factor and should stay outside unless the expression specifically asks for it inside.

🔄 Real-world variant

If the expression were $-3x^{5/3}$, you would rewrite it as $-3\sqrt[3]{x^5}$. If the exponent had a different denominator, such as $x^{2/5}$, the radical would use a fifth root instead of a cube root.

🔍 Related terms

fractional exponents, radical form, cube root