Rewrite the exponential expression as a radical expression.

Key takeaway: To rewrite a fractional exponent as a radical, use the rule $x^{m/n}=\sqrt[n]{x^m}$. The coefficient stays outside the radical.

Use the fractional-exponent rule:

$x^{m/n}=\sqrt[n]{x^m}$

Here,

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

So

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

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

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Pitfalls the pros know 👇 A common mistake is to put the negative sign inside the radical or to write a square root instead of a cube root. The denominator of the exponent tells you the index of the radical.

What if the problem changes? If the expression were $3x^{2/3}$, the radical form would be $3\sqrt[3]{x^2}$. If it were $-3x^{1/2}$, then it would become $-3\sqrt{x}$.

Tags: fractional exponent, cube root, radical expression