Question

Simplify using laws of exponents : $\frac{100\times 3^3\times 25\times 32}{5^2\times 2^4\times 10}$

Answer 1

$\frac{100\times 3^3\times 25\times 32}{5^2\times 2^4\times 10}$

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

$=\frac{5^2\times 2^2\times 3^3\times 5^2\times 2^5}{5^3\times 2^5}$

$=\frac{5^4\times 2^7\times 3^3}{5^3\times 2^5}$

$=5^{4-3}\times 2^{7-5}\times 3^3$

$=5\times 2^2\times 3^3$