Question

solve it please................​

Answer 1

question:

$\sf \frac{ {5}^{ - 7} \times {( - 2)}^{3} }{2 \times \frac{5}{ - 5} }$

solution:

$\pink{\sf \frac{ {5}^{ - 7} \times {( - 2)}^{3} }{2 \times \frac{5}{ - 5} } = -0.16 }$

To find:

$\sf value \: of \: \frac{ {5}^{ - 7} \times {( - 2)}^{3} }{2 \times \frac{5}{ - 5} } \: ?$

step by step explanation:

$\implies\sf \frac{ {5}^{ - 7} \times {( - 2)}^{3} }{2 \times \frac{5}{ - 5} }$

$\implies\sf \frac{{\cancel 5}\times{\cancel 5}\times{\cancel 5}\times{\cancel 5}\times{\cancel 5}{( - 2)}^{3} }{2 \times {\cancel 5}\times{\cancel 5}\times{\cancel 5}\times{\cancel 5}\times{\cancel 5}\times 5 \times 5}$

$\implies \sf \frac{{( - 2)}^{3} }{2 \times 5 \times 5}$

$\implies \sf \frac{( - 2) \times ( - 2) \times ( - 2) }{2 \times {5}^{2} }$

$\implies \sf \frac{( - 2) \times ( { \cancel- 2)} \times ( { \cancel- 2)} }{2 \times 25}$

$\implies \sf \frac{( - 2) \times 4 }{2 \times 25 }$

$\implies \sf \frac{( - 2) \times { \cancel4 }}{{ \cancel2} \times 25 }$

$\implies \sf \frac{( - 2) \times 2}{1 \times 25 }$

$\implies \sf \frac{ - 4}{25 }$

$\implies \sf - 0.16$

therefore:

$\implies \purple{\sf \frac{ {5}^{ - 7} \times {( - 2)}^{3} }{2 \times \frac{5}{ - 5} } = -0.16}$

Answer 2

$\red{\Large \bf Solution :}$

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$\bf \dfrac{5^{-7} \times (-2)^{3}}{2 \times 5^{-5}}$

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$\bf We \: know \: that \: a^{-m} = \dfrac{1}{a^m}$

$\bf \implies \dfrac{\dfrac{1}{5^{7}} \times (-2)^{3}}{2 \times \dfrac{1}{5^{5}}}$

$\bf \implies \dfrac{\dfrac{1}{5^{7}} \times (-2) \times (-2) \times (-2)}{\dfrac{2}{5^{5}}}$

$\bf \implies \dfrac{\dfrac{1}{5^{7}} \times (-8)}{\dfrac{2}{5^{5}}}$

$\bf \implies \dfrac{\dfrac{-8}{5^{7}}}{\dfrac{2}{5^{5}}}$

$\bf \implies \dfrac{-8}{5^{7}} \times \dfrac{5^5}{2}$

$\bf \implies \dfrac{-8}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5} \times \dfrac{5 \times 5 \times 5 \times 5 \times 5}{2}$

$\bf \implies \dfrac{-8}{\cancel{5} \times \cancel{5} \times \cancel{5} \times \cancel{5} \times \cancel{5} \times 5 \times 5} \times \dfrac{\cancel{5} \times \cancel{5} \times \cancel{5} \times \cancel{5} \times \cancel{5}}{2}$

$\bf \implies \dfrac{\cancel{-8}^{-4}}{5 \times 5 \times \cancel{2}}$

$\bf \implies \dfrac{-4}{25}$

$\bf \implies - 0.16$

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$\pink{\bf \therefore \: Answer \: is \: - 0.16}$