Question

25*5²*t^8/10³*t^3. ​

Answer 1

$\bold {\huge{\red{\underline{\underline{Answer:}}}}} \\ \frac{ 25 \times 5 {}^{2} \times t {}^{8} }{10 {}^{3} \times t {}^{3} } \\ = \frac{5 {}^{2} \times 5 {}^{2} \times t {}^{8} }{(2 \times 5) {}^{3} \times {t}^{3} } \\ = \frac{5 {}^{2 + 2} \times {t}^{8} }{2 {}^{3} \times 5 {}^{3} \times {t}^{3} } \: \: \: \: (a {}^{m} \times a {}^{n} = a {}^{m + n} ) \\ = 5 {}^{4} \times {t}^{8} \times 2 { }^{ - 3} \times 5 ^{ - 3} \times {t}^{ - 3} \\ =5^{4+(-3)}×t^{8+(-3)}×2^{-3} \\ =5^{4-3}×t^{8-3}× \frac{1}{8} \: \: \: \: \: \: \: (x^{-n}= \frac{1}{x^{n}}) \\ = \frac{ 5t^{5}}{8}$

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