Question

Simplify:$\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

• A. $a^{11}{b}^{18}{c}^{-15}$
• B. $a^{-11}{b}^{18}{c}^{-15}$
• C. $a^{11}{b}^{18}{c}^{15}$
• D. $a^{-11}{b}^{-18}{c}^{15}$

Answer 1

The correct option is B $a^{-11}{b}^{18}{c}^{-15}$

$\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

Using $a^m\times a^n=a^{m+n}$

$=\frac{a^{1+4}{b}^{2+5}{c}^{3-6}}{a^{-7+10+13}{b}^{-8+11-14}{c}^{9-12+15}}$

$=\frac{a^5{b}^7{c}^{-3}}{a^{16}{b}^{-11}{c}^{12}}$

Using $\frac{a^m}{a^n}=a^{m-n}$

$=a^{5-16}{b}^{7-(-11)}{c}^{-3-12}$

$=a^{-11}{b}^{7+11}{c}^{-15}$

$=a^{-11}{b}^{18}{c}^{-15}$