Question

Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Answer 1

$=\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

$=\frac{\left(45x^{-4}\right)}{(5^{-4}\times 2^2\times 5^2\times x^{-8})}[a^m\times b^m=(ab{)}^m]$


$=\frac{\left(45x^{-4-(-8)}\right)}{(5^{(-4+2)}\times 2^2)}[a^m÷a^n=a^{m-n}and{a}^m\times a^n=a^{m+n}]$

$=\frac{\left(45x^4\right)}{(5^{-2}\times 2^2)}$

$=\frac{(45x^4\times 25)}{4}$

$=\frac{\left(1125x^4\right)}{4}$

$Substitutingx=6$

$=\frac{\left[1125\right(6^4\left)\right]}{4}$

$=\frac{(1125\times 1296)}{4}$

$=364500$

$=3.645\times {10}^5$