Question
Simplify :
$\frac{25 \times 5^2 \times t^8}{10^3 \times t^4}$
$\frac{25 \times 5^2 \times t^8}{10^3 \times t^4}$
✓
Answer
We have, $\frac{25 \times 5^2 \times t^8}{10^3 \times t^4}=\frac{5^2 \times 5^2 \times t^8}{(2 \times 5)^3 \times t^4}$ $\left[\because 25=5 \times 5=5^2\right.$ and $\left.10=2 \times 5\right]$
$=\frac{5^{2+2} \times t^8}{2^3 \times 5^3 \times t^4} \quad\left[\begin{array}{l}\because a^m \times a^n=a^{m+n} \\ \text { and }(a b)^m=a^m \times b^m\end{array}\right]$
$=\frac{5^{4-3} \times t^{8-4}}{2^3}=\frac{5 \times t^4}{2 \times 2 \times 2}=\frac{5 t^4}{8}$ $\left[\because a^m \div a^n=a^{m-n}\right]$
$=\frac{5^{2+2} \times t^8}{2^3 \times 5^3 \times t^4} \quad\left[\begin{array}{l}\because a^m \times a^n=a^{m+n} \\ \text { and }(a b)^m=a^m \times b^m\end{array}\right]$
$=\frac{5^{4-3} \times t^{8-4}}{2^3}=\frac{5 \times t^4}{2 \times 2 \times 2}=\frac{5 t^4}{8}$ $\left[\because a^m \div a^n=a^{m-n}\right]$
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