Question

Solve :$\frac{16\times {10}^4\times 3^3}{6^5\times 5^6}$

Answer 1

$\frac{16\times {10}^4\times 3^3}{6^5\times 5^6}$

$\Rightarrow \frac{(2{)}^4\times (5\times 2{)}^4\times 3^3}{(2\times 3{)}^5\times 5^6}$

$\Rightarrow \frac{2^4\times 5^4\times 2^4\times 3^3}{2^5\times 3^5\times 5^6}$

$\Rightarrow 2^{4+4-5}\times 5^{4-6}\times 3^{3-5}$

$\Rightarrow 2^3\times 5^{-2}\times 3^{-2}$

$\Rightarrow \frac{2^3}{5^2\times 3^2}=\frac{8}{25\times 9}=\frac{8}{225}$.