Question

Simplify:
$\frac{25\times t^{-4}}{5^{-3}\times 10\times t^{-8}}where,(t\ne 0)$

Answer 1

$\frac{25\times t^{-4}}{5^{-3}\times 10\times t^{-8}}=\frac{5^2\times t^{-4}}{5^{-3}\times 5\times 2\times t^{-8}}=\frac{5^{2-(-3)-1}\times t^{-4-(-8)}}{2}[\because a^m÷a^n=a^{m-n}]=\frac{5^{2+3-1}\times t^{-4+8}}{2}=\frac{5^4\times t^4}{2}=\frac{625}{2}{t}^4$