Question

$\frac{\left(2p^2{q}^9{)}^2\right(4pq{)}^3}{(4p^6{q}^{10}{)}^2}$

Answer 1

$\frac{{\left(2p^2{q}^9\right)}^2{\left(4pq\right)}^3}{{\left(4p^6{q}^{10}\right)}^2}$

$=\frac{2^2\times p^4\times q^{18}\times {\left(2^2\right)}^2\times p^3\times q^3}{{\left(2^2\right)}^2\times p^{12}\times q^{20}}$

$=\frac{2^2\times p^4\times q^{18}\times 2^4\times p^3\times q^3}{2^4\times p^{12}\times q^{20}}$

$=2^{2+4-4}\times p^{4+3-12}\times q^{18+3-20}$

$=2^2\times p^{-5}\times q^1$

$=\frac{4q}{p^5}$