Question

Which of the following has a negative index?

• A. ${\left(x\right)}^{\frac{1}{4}}$
• B. ${\left(x\right)}^{\frac{2}{3}}$
• C. $\frac{1}{x^2}$
• D. ${(-x)}^{\frac{2}{3}}$

Answer 1

The correct option is C $\frac{1}{x^2}$

Option A has positive index i.e. $\frac{1}{4}$.

Option B also has positive index i.e., $\frac{2}{3}$

In option C, $\frac{1}{x^2}=x^{-2}$.

Index of $x$ is $(-2)$, which is negative.

Hence, option C is correct