Question

Simplify:
$\frac{\left[\right(-5{)}^3{]}^4\times 8^2}{4^3\times (25{)}^5}$

Answer 1

Given $\frac{\left[\right(-5{)}^3{]}^4\times 8^2}{4^3\times (25{)}^5}$
$=\frac{(-5{)}^{3\times 4}\times (2^3{)}^2}{(2^2{)}^3\times (5^2{)}^5}$ [Since, $(a^m{)}^n=a^{m\times n}$ ]
$=\frac{(-5{)}^{12}\times 2^6}{2^6\times 5^{10}}$
$=\frac{(-1{)}^{12}(5{)}^{12}\times 2^6}{2^6\times 5^{10}}$ [Since, $(ab{)}^m=a^m\times b^m$]
$=1\times 5^{12-10}\times 2^{6-6}$ [Since, $\frac{a^m}{a^n}=a^{m-n}$]
$=5^2\times 2^0$
$=25\times 1$ [Since, $a^0=1$ for any non zero quantity of $a$]
$=25$