Question

x³·x⁻⁵, options: x², x⁻³, x⁻¹, x⁻²

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule $a^m \cdot a^n = a^{m + n}$. Here, the base is $x$, $m = 3$, and $n=-5$.
$$x^{3} \cdot x^{-5}=x^{3 + (-5)}$$

Step2: Simplify the exponent

Calculate $3+(-5)=3 - 5=-2$. So we have $x^{-2}$.

Answer:

$\boldsymbol{x^{-2}}$ (corresponding to the teal-colored option with $x^{-2}$)