Question

solve it please math​

Answer 1

Given :

$\red \bigstar \rm \: simplify : \\ \\ \rm \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} }$

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To Find :

•The remainder from this question =?

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Solution :

$\green{\bold{\underline{\underline{Step \: by \: step \: explanation :}}}}$

$\\ \implies \sf \: \frac{ {3}^{5} \times {10}^{5} \times 125 }{ {5}^{7} \times {6}^{5} } \\ \\ \implies \sf \: \: \frac{3 \times 3 \times 3 \times 3 \times 3 \times {10}^{5} \times 5 \times 5 \times 5}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 6 \times 6 \times 6 \times 6 \times 6} \\ \\ \\ \implies \sf \: \frac{ \cancel3 \times \cancel3 \times \cancel3 \times \cancel3 \times \cancel3 \times {10}^{5} \times \cancel5 \times \cancel5 \times \cancel5}{ \cancel5 \times \cancel5 \times \cancel5 \times 5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \frac{ {10}^{5} }{5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \: \frac{100000}{5 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \frac{20000}{5 \times 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \: \frac{4000}{5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \frac{800}{5 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \\ \implies \sf \: \frac{160}{2 \times 2 \times 2 \times 2 \times 2 } \\ \\ \\ \implies \sf \: \frac{160}{4 \times 8} \\ \\ \\ \implies \sf \: \frac{40}{8} \\ \\ \implies \boxed{ \sf{5}}$

➡ The Correct answer will be 5.

Answer 2

Given :

• $\rm\sf\frac{3^5 × 10^5 × 125}{5^7 × 6^5}$

According to the question :

⟹ $\sf\frac{3^5 × 10^5 × 125}{5^7 × 6^5}$

⟹ $\sf\frac{( 3 × 3 × 3 × 3 × 3 ) × ( 10^5) × ( 5^3)}{( 5 × 5 × 5 × 5 × 5 × 5 × 5 ) × ( 6 × 6 × 6 × 6 × 6)}$

⟹ $\sf\frac{( 3 × 3 × 3 × 3 × 3 ) × ( 10^5) × ( 5 × 5 × 5)}{( 5 × 5 × 5 × 5 × 5 × 5 × 5 ) × ( 6 × 6 × 6 × 6 × 6)}$

⟹ $\sf\frac{(3 × 3 × 3 × 3 × 3 ) × ( 10^5) × ( 5 × 5 × 5 )}{( 5 × 5 × 5 × 5 × 5 × 5 × 5 ) × ( 6 × 6 × 6 × 6 × 6)}$

⟹ $\sf\frac{( 10^5)}{( 5 × 5 × 5 × 5 × 5 ) × ( 2 × 2 × 2 × 2 × 2)}$

⟹ $\sf\frac{( 100000)}{(5 × 5 × 5 × 5 × 5 ) × ( 2 × 2 × 2 × 2 × 2 )}$

⟹ $\sf\frac{( 20000)}{( 5 × 5 × 5 × 5 ) × ( 2 × 2 × 2 × 2 × 2 )}$

⟹ $\sf\frac{( 4000 )}{( 5 × 5 × 5 ) × ( 2 × 2 × 2 × 2 × 2)}$

⟹ $\sf\frac{( 800 )}{( 5 × 5 ) × ( 2 × 2 × 2 × 2 × 2)}$

⟹ $\sf\frac{( 160 )}{( 5 ) × ( 2 × 2 × 2 × 2 × 2)}$

⟹ $\sf\frac{( 160 )}{( 2 × 2 × 2 × 2 × 2)}$

⟹ $\sf\frac{160}{2 × 2 × 2 × 2 ×2}$

⟹ $\sf\frac{160}{32}$

⟹ $\sf\frac{160}{32}$

⟹ $\sf\bold{5}$

So, It's Done !!