Question

$\text{Solve:}$ ${\left(\frac{1}{4{ab}^{2}c}\right)}^2÷{\left(\frac{3}{2a^2{bc}^2}\right)}^4$

Answer 1

${\left(\frac{1}{4a{b}^{2}c}\right)}^2÷{\left(\frac{3}{2a^{2}b{c}^2}\right)}^4$

$=\frac{1}{16a^2{b}^4{c}^2}\times \frac{16a^8{b}^4{c}^8}{81}$ [$\because \frac{a}{b}÷\frac{c}{d}$ $=$ $\frac{a}{b}\times \frac{d}{c}$]

$=\frac{1}{81}{a}^{8-2}{b}^{4-4}{c}^{8-2}$ [$\because a^m÷a^n=a^{m-n}$]

$=\frac{1}{81}{a}^6{b}^0{c}^6$ [$\because a^0=1$]

$=\frac{a^6{c}^6}{81}$

$=\frac{\left(a^3{)}^2\right(c^3{)}^2}{9^2}$

$=(\frac{a^3{c}^3}{9}{)}^2$