Question

Simplify this

$\\ \sf \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} }$​

Answer 1

$\:\:\:\: \large\underline {\sf{To\:Simplify\::}}$

$\\ \sf \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} }$

$\:\:\:\: \large\underline {\sf{Solution \::}}$

$\\ :\implies \sf \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} }$

$\\ :\implies \sf \: \: \frac{3 \times 3 \times 3 \times 3 \times 3 \times {10}^{5} \times 5 \times 5 \times 5}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 6 \times 6 \times 6 \times 6 \times 6}$

$\\ :\implies \sf \: \frac{ \cancel3 \times \cancel3 \times \cancel3 \times \cancel3 \times \cancel3 \times {10}^{5} \times \cancel5 \times \cancel5 \times \cancel5}{ \cancel5 \times \cancel5 \times \cancel5 \times 5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ : \implies \sf \: \frac{ {10}^{5} }{5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ :\implies \sf \: \: \frac{100000}{5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ : \implies \sf \: \frac{20000}{5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ :\implies \sf \: \: \frac{4000}{5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ :\implies \sf \: \frac{800}{5 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\\ :\implies \sf \: \frac{160}{2 \times 2 \times 2 \times 2 \times 2 }$

$\\ :\implies \sf \: \frac{160}{4 \times 8}$

$\\ :\implies \sf \: \frac{40}{8}$

$:\implies{\boxed{\sf{\red{ 5}}}}$

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Answer 2

• $\\ \sf \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} }$