Question

25 into T-4
5-3into 10 into t-8​

Answer 1

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

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

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

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

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

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

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

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

= 3°×2°×5^5. (a°=1)

$= {5}^{5}$

I HOPE IT HELPS ☺️ FOLLOW ME DUDE