Question

How do you solve x^-1(x^-2+x^-3)?

Answer 1

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ x^{-1}(x^{-2}+x^{-3})\impliedby \textit{first we distribute} \\\\\\ x^{-1}\cdot x^{-2}+x^{-1}\cdot x^{-3}\impliedby \textit{same base, add the exponents} \\\\\\ x^{-1-2}+x^{-1-3}\implies x^{-3}+x^{-4}\implies \cfrac{1}{x^3}+\cfrac{1}{x^4}$

Answer 2

D.  I would add the exponents   

x^a ( x^b + x^c)  =  (x^(a+b)) + (x^(a+c))    

Then know    x^-a =   1/(x^a)