Question

Simplify $\frac{{\left(1024\right)}^3\times {\left(81\right)}^4}{{\left(243\right)}^2\times {\left(128\right)}^4}$

Answer 1

Observe $1024=2^{10}$, $81=3^4$, $243=3^5$, and $128=2^7$. Hence the expression is
$\frac{{\left(2^{10}\right)}^3\times {\left(3^4\right)}^4}{{\left(3^5\right)}^2\times {\left(2^7\right)}^4}=\frac{{\left(2\right)}^{30}\times {\left(3\right)}^{16}}{{\left(3\right)}^{10}\times {\left(2\right)}^{28}}$
$=2^{30-28}\times 3^{16-10}=2^2\times 3^6=2916$