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Simplify : \( \frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}} \)
Given: $\frac{25 \times 5^{2} t^{8}}{10^{3} t^{4}}$
To do: We have to simplify
Solution:
$\frac{25 \times 5^{2} t^{8}}{10^{3} t^{4}}$
Cancel $\frac{25 \times 5^{2} t^{8}}{10^{3} t^{4}}: \frac{5^{2} \times 25 t^{4}}{10^{3}}$
$=\frac{5^{2} \times 25 t^{4}}{10^{3}}$
Factor $10^{3}: 2^{3} \times 5^{3}$
Factor $25: \quad 5^{2}$
$=\frac{5^{2} \times 5^{2} t^{4}}{2^{3} \times 5^{3}}$
$5^{2} \times 5^{2} t^{4}=5^{4} t^{4}$
$=\frac{5^{4} t^{4}}{2^{3} \times 5^{3}}$
Cancel $\frac{5^{4} t^{4}}{2^{3} \times 5^{3}}: \frac{5 t^{4}}{2^{3}}$
$=\frac{5 t^{4}}{2^{3}}$
$2^{3}=8$
$=\frac{5 t^{4}}{8}$
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