Question

Solve: $\frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}$

Answer 1

$\frac{{12}^9\times 9^3\times 4}{6^3\times 8^2\times 27}=\frac{(3\times 4{)}^4\times (3^2{)}^3\times 4}{(3\times 2{)}^3\times (4\times 2{)}^2\times \left(3^3\right)}$

$=\frac{3^4\times 4^4\times 3^6\times 4}{3^3\times 2^3\times 4^2\times 2^2\times 3^3}$

$=\frac{3^4\times (2^2{)}^4}{2^3\times (2^2{)}^2}=\frac{3^4\times 2^8}{2^7}=2\times 3^4$

$=2\times (9{)}^2=81\times 2=162$

$\therefore \frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}=162$