Question

simplify the following
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Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{ Question }}}}$


$\bf{ To \: Solve \: : \: \frac{ {3}^{ - 5} \times {10}^{ - 4} \times {5}^{4} }{ {5}^{2} \times {6}^{ - 5} } }$


$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$


$= \: \frac{ {3}^{ - 5} \times {10}^{ - 4} \times {5}^{4} }{ {5}^{2} \times {6}^{ - 5} }$

$= \: \frac{ {3}^{ - 5} \times ( {5}^{ - 4} \times \: {2}^{ - 4}) \times {5}^{4} }{ {5}^{2} \times {6}^{ - 5} }$

$= \: \frac{ {3}^{ - 5} \times {5}^{ - 4} \times {5}^{4} \times {2}^{ - 4} }{ {5}^{2} \times ( {2}^{ - 5} \times {3}^{ - 5}) }$

$= \: \frac{ {3}^{ - 5} \times {5}^{( - 4 + 4)} \times {2}^{ - 4} }{ {5}^{2} \times {2}^{ -5 }\times {3}^{ - 5} } \: \: \: (using \: identity \: : {x}^{a} \times {x}^{b} = {x}^{(a + b)} )$

$= \frac{ {3}^{ - 5} \times \: {5}^{0} \: \times \: {2}^{ - 4} }{ {5}^{2} \times \: {2}^{ - 5} \times {3}^{ - 5} }$

$= \: \frac{ {5}^{0} \: \times \: {2}^{ - 4} }{ {5}^{2} \times \: {2}^{ - 5} }$

$= {5}^{0 - 2} \times {2}^{ (- 4) - ( - 5)} \: \: \: \: \: \: \: \: \: \:( using \: \frac{ {x}^{a} }{ {x}^{b}} = {x}^{(a - b)} )$

$= {5}^{ - 2} \: \times \: {2}^{ 1}$

$= \: {5}^{ - 2} \: \times 2$

$= \: 0.04 \: \times 2$

$= \: 0.08$