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

Q: What is the radical form of $-3x^{2/3}$?

The radical form is $-3\sqrt[3]{x^2}$. The exponent $2/3$ means cube root of $x^2$, and the coefficient $-3$ stays outside.

Q: Can the $-3$ be placed inside the radical?

Not in the direct rewrite. Moving $-3$ inside the radical changes the expression unless it is rewritten using a valid equivalent form.

Question

Rewrite the exponential expression as a radical expression.

$-3x^{2/3}$

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

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

Acemy AI · Accepted Answer

> **Expert intro**: Use the fractional exponent rule and keep the negative coefficient separate from the radical unless the problem asks otherwise.

### Detailed walkthrough
Start with the exponent rule:

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

Now multiply by $-3$:

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

Therefore, the radical expression is

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

### 💡 Pitfall guide
Do not write $\sqrt[3]{-3x^2}$ unless the coefficient has been intentionally moved inside the radical. That changes the value of the expression.

### 🔄 Real-world variant
If the exponent were $5/3$, the radical form would be $-3\sqrt[3]{x^5}$. If the denominator were $2$, the expression would use a square root instead of a cube root.

### 🔍 Related terms
fractional exponent, radical notation, cube root

Question

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

Expert Verified Solution

Detailed walkthrough

💡 Pitfall guide

🔄 Real-world variant

🔍 Related terms

FAQ

What is the radical form of $-3x^{2/3}$?

Can the $-3$ be placed inside the radical?