Rewrite the radical expression as an exponential expression: $-\sqrt[3]{2x^8}$

Expert intro: To rewrite a radical as an exponential expression, convert the radical index to a rational exponent and keep any outside negative sign unchanged.

Detailed walkthrough

We use the rule

$\sqrt[n]{a}=a^{\frac{1}{n}}$

So

$-\sqrt[3]{2x^8} = -(2x^8)^{\frac{1}{3}}$

This keeps the negative sign in front and rewrites the cube root as an exponent.

💡 Pitfall guide

A common mistake is to write the negative sign inside the radical without reason. The expression is already negative outside, so the correct exponential form is $-(2x^8)^{1/3}$, not $(-2x^8)^{1/3}$.

🔄 Real-world variant

If the expression were $\sqrt[3]{-2x^8}$, then the negative would be inside the base. That would be written as $(-2x^8)^{1/3}$.

🔍 Related terms

rational exponents, cube root, radical notation