Question

Simplify the following

${\displaystyle \frac{4a{b}^2(-5a{b}^3)}{10a^2{b}^2}}$

Answer 1

${\displaystyle \frac{4a{b}^2(-5a{b}^3)}{10a^2{b}^2}}$

${\displaystyle =\frac{4\times a\times b^2\times (-5)\times a\times b^3}{10a^2{b}^2}}$

${\displaystyle =\frac{-20\times a^1\times a^1\times b^2\times b^3}{10a^2{b}^2}}$

${\displaystyle =\frac{-20\times a^{1+1}\times b^{2+3}}{10a^2{b}^2}}$

${\displaystyle =-2\times a^2\times b^5\times a^{-2}\times b^{-2}}$

${\displaystyle =-2\times a^{2+(-2)}\times b^{5+(-2)}}$

${\displaystyle =-2\times a^0\times b^3}$

${\displaystyle =-2b^3}$