Question

Simplify and express the answer in the positive exponent form:​
(ii) $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}$

Answer 1

Given, $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}$
It can be written as:
$\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}=\frac{2^{3\times 5}\times 5^4}{(2\times 2{)}^3\times 5^2}$
On further calculation , we have :

$\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}=\frac{2^{15}\times 5^4}{2^6\times 5^2}$

[$\because$ $a^m\times a^n=a^{m+n}$]

$=(2{)}^{15-6}\times 5^{4-2}$

$=2^9\times 5^2$

Hence, $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}=2^9\times 5^2$.