Question

Simplify : $\frac{25\times t^4}{5^{-3}\times 10\times t^{-8}}$

Answer 1

Let $a=\frac{25\times t^4}{5^{-3}\times 10\times t^{-8}}$

$=\frac{5^{2+3}\times t^{4+8}}{10}$ using $\frac{a^m}{a^n}=a^{m-n}$

$=\frac{5^5\times t^{12}}{5\times 2}$

$=\frac{5^4}{2}\times t^{12}$

$=\frac{625}{2}\times t^{12}$

$a=\frac{625t^{12}}{2}$

$\frac{25\times t^4}{5^{-3}\times 10\times t^{-8}}=\frac{625t^{12}}{2}$