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

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

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

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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Updated on: 10-Oct-2022

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