Question

Evaluates the following.
$\frac{(5^3{)}^3\times (2\times 5{)}^3\times 2^4}{5^7\times (2^2{)}^2\times 5^8}$

Answer 1

$\frac{(5^3{)}^3\times (2\times 5{)}^3\times 2^4}{5^7\times (2^2{)}^2\times 5^8}=\frac{5^9\times 2^3\times 5^3\times 2^4}{5^7\times 2^4\times 5^8}$ (since, $(a^m{)}^n=a^{mn}$)

$=\frac{5^{12}\times 2^7}{5^{15}\times 2^4}$ (since, $a^m\times a^n=a^{m+n}$)

$=5^{-3}\times 2^{-3}$ (since, $\frac{a^m}{a^n}=a^{m-n}$)

$=(5\times 2{)}^{-3}={10}^{-3}=0.001$