which expression is equivalent to $4x^{-2}+3x^{-5}$?\na. $7x^{-7}$\nb. $12x^{10}$\nc. $\frac{7}{x^{7}}$\nd…

Explanation:

Step1: Rewrite with positive exponents

Recall $a^{-n}=\frac{1}{a^{n}}$. So $4x^{-2}=\frac{4}{x^{2}}$ and $3x^{-5}=\frac{3}{x^{5}}$.

Step2: Find a common - denominator

The common denominator of $\frac{4}{x^{2}}$ and $\frac{3}{x^{5}}$ is $x^{5}$. Rewrite $\frac{4}{x^{2}}$ as $\frac{4x^{3}}{x^{5}}$ (by multiplying numerator and denominator by $x^{3}$).

Step3: Add the fractions

$\frac{4x^{3}}{x^{5}}+\frac{3}{x^{5}}=\frac{4x^{3}+3}{x^{5}}$

Answer:

D. $\frac{4x^{3}+3}{x^{5}}$