-3x^{2/3}

Expert intro: This is a direct rational-exponent conversion. The exponent $2/3$ means cube root of the square, and the coefficient stays outside.

Detailed walkthrough

Use the rule

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

So

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

That is the correct radical form:

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

You can also verify that this keeps the value unchanged for real $x$.

💡 Pitfall guide

Do not rewrite it as $\sqrt[3]{-3x^2}$ unless the original expression is exactly inside the radical. Also, do not change the exponent $2/3$ into a square root; the denominator 3 means cube root.

🔄 Real-world variant

If the coefficient were positive, $3x^{2/3}=3\sqrt[3]{x^2}$. If the exponent were $1/3$, then the expression would be $-3\sqrt[3]{x}$.

🔍 Related terms

cube root, fractional exponent, coefficient