Question

Simplify:
$\frac{25\times 5^2\times t^8}{{10}^3\times t^4}$

Answer 1

$\frac{25\times 5^2\times t^8}{{10}^3\times t^4}$

$=$ $\frac{5^2\times 5^2\times t^8}{{10}^3\times t^4}$

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

$=$ $\frac{5^4\times t^8}{{10}^3\times t^4}$

$=$ $\frac{5^4\times t^{(8-4)}}{{10}^3}$ [ $\because \frac{a^m}{a^n}=a^{m-n},a\ne 0$ ]

$=$ $\frac{625\times t^4}{1000}$

$=$ $0.625t^4$

$\therefore \frac{25\times 5^2\times t^8}{{10}^3\times t^4}=0.625t^4$