Question

what is it equivalent to? $sqrt3{-x}$
a $(-x)^3$
b $x^{-3}$
c $(-x)^{\frac{1}{3}}$
d $x^{-\frac{1}{3}}$

Explanation:

Step1: Recall root to exponent rule

A cube root $\sqrt[3]{a}$ equals $a^{\frac{1}{3}}$.

Step2: Apply rule to the given expression

Substitute $a=-x$ into the rule: $\sqrt[3]{-x}=(-x)^{\frac{1}{3}}$.

Step3: Match with options

Compare to the provided choices to find the equivalent form.

Answer:

C. $(-x)^{\frac{1}{3}}$