Question

(3a^-4/ 2b^-3)^-2 * 10a^7b^3

Answer 1

$( \frac{3a^{-4}}{2b^{-3}} )^{-2} * 10a^7b^3= \frac{(3a^{-4})^{-2}}{(2b^{-3})^{-2}} *10a^7b^3= \frac{3^{-2}*a^8*10a^7b^3}{2^{-2}*b^6} =$

$= \frac{3^{-2}*10*a^{8+7}*b^3}{2^{-2}*b^6} =\frac{3^{-2}*5*2*a^{15}*b^3}{2^{-2}*b^6} =3^{-2}*5*2^{1+2}*a^{15}*b^{3-6}=$

$= \frac{1}{3^2} *5*2^3*a^{15}*b^{-3}= \frac{5*8*a^{15}}{9*b^3} = \frac{40a^{15}}{9b^3}$