1.

25 into T-45-3into 10 into t-8​

Answer»

i). \frac{25 \times t {}^{ - 4} }{ {5}^{2} \times 10 \times {t}^{ - 8} } = \frac{ {5}^{2} + {t}^{ - 4} }{ {5}^{ - 3} \times 5 \times 2 \times {t}^{ - 8} }

= \frac{ {5}^{2} \times {t}^{ - 4} }{ {5}^{ - 3 + 1} \times 2 \times {t}^{ - 8} } ( {a}^{m} \times {a}^{n} = {a}^{m + n)}

\frac{ {5}^{2} \times {t}^{ - 4} }{ {5}^{ - 2} \times 2 \times {t}^{ - 8} }

= \frac{ {5}^{2 - ( - 2)} {t}^{ - 4 - ( - 8)} }{2} ( {a}^{m} \div {a}^{n} = {a}^{m - n} )

= \frac{ {5}^{4} {t}^{4} }{2} = \frac{625 {t}^{4} }{2}

ii). \frac{ {3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} } = \frac{ {3}^{ - 5} \times (2 \times 5) {}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times (2 \times 3) {}^{ - 5} }

= \frac{ {3}^{ - 5} \times {2}^{ - 5} \times {5}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times {2}^{ - 5} \times {3}^{ - 5} } (a \times b) {}^{m} = {a}^{m} \times {b}^{m}

= {3}^{ - 5 - ( - 5)} \times {2}^{ - 5 - ( - 5)} \times {5}^{ - 5 + 3 - ( - 7)} ( {a}^{m} \div {a}^{n} = {a}^{m - n} )

= 3°×2°×5^5. (a°=1)

= {5}^{5}

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