Question

Can anyone plz solve and explain it to me
$\frac{25 \times {x}^{ - 4} }{ {5}^{ - 3} \times 10 \times {x}^{ - 8} }$
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Answer 1

$\: \: \: \: \frac{25 \times {x}^{ - 4} }{ {5}^{ - 3} \times 10 \times {x}^{ - 8} } \\ \\= \frac{25 \times {5}^{3} \times {x}^{8} }{5 \times 2 \times {x}^{4} } \\ \\ = \frac{ {5}^{2} \times {5}^{2} \times {x}^{4} }{2} \\ \\ = \frac{625 \times {x}^{4} }{2} \\ \\ = 312.5 \times {x}^{4}$

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \:SOLUTION \: \: \red{ \mid}}}}}}}}$

$\underline{ \underline{ \bold{ \red{ \: \: \: \: IDENTITIES \: \: \: \: USED \: \: \: \: }}}}$



$\bold{ \red{1.} \: \: \: \: a {}^{m} \times a {}^{n} = a {}^{m + n } } \\ \\ \bold{ \red{2.} \: \: \: \: \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n} } \\ \\ \bold{ \red{3.} \: \: \: \: a {}^{ - n} = \frac{1}{a {}^{n} } }$


_______________________________


$\bold{ \frac{25 \times x {}^{ - 4} }{5 {}^{ - 3} \times 10 \times x {}^{ - 8} } } \\ \\ \bold{ = \frac{5 {}^{2} \times x {}^{ - 4} }{5 {}^{ - 3} \times 5 \times 2 \times x {}^{ - 8} } } \\ \\ \bold{ = \frac{5 {}^{2} \times x {}^{ - 4} }{5 {}^{ - 3 + 1} \times 2 \times x {}^{ - 8} }} \\ \\ \bold{ = \frac{5 {}^{2} \times x {}^{ - 4} }{5 {}^{ - 2} \times 2 \times x {}^{ - 8} } } \\ \\ \bold{ = \frac{1}{2} \times \frac{5 {}^{2} }{5 {}^{ - 2} } \times \frac{x {}^{ - 4} }{ x {}^{ - 8} } } \\ \\ \bold{ = \frac{1}{2} \times 5 {}^{2 - ( - 2)} \times x {}^{ - 4 - ( - 8)} } \\ \\ \bold{ = \frac{1}{2} \times 5 {}^{2 + 2} \times x {}^{ - 4 + 8} } \\ \\ \bold{ = \frac{1}{2} \times 5 {}^{4} \times x {}^{4} } \\ \\ \bold{ = \frac{1}{2} \times 625 \times x {}^{4} } \\ \\ \bold{ = \underline{ \red{ \: 312.5 \times x {}^{4} \: }}}$

$\underline{ \underline{ \huge{ \pink{ \mathbb{ \: \: OR \: \: }}}}}$


$\bold{ \frac{25 \times x {}^{ - 4} }{5 {}^{ - 3} \times 10 \times x {}^{ - 8} } } \\ \\ \bold{ = \frac{5 {}^{2} \times 5 {}^{3} \times x {}^{ - 4} \times x {}^{8} }{10 } } \\ \\ \bold{ = \frac{5 {}^{(2 + 3)} \times x {}^{(- 4 + 8)} }{10} } \\ \\ \bold{ = \frac{5 {}^{5} \times x {}^{4} }{10} } \\ \\ \bold{ = \frac{5 {}^{5} }{10} \times x {}^{4} } \\ \\ \bold{ = \frac{3125}{10} \times x {}^{4} } \\ \\ \bold{ = \underline{ \red{ \: 312.5 \times x {}^{4} \: }}}$