Question

27 raised by 2 x minus M raised by 5 n and raised by 2 / 18 raised by 3 X m raised by 3 n

Answer 1

$\bold{Now,}$

$\frac{ {27}^{3} \times { (- m)}^{5} n }{ {18}^{3} \times {m}^{3} n}$

$= \frac {({3}^{3})^{2}\times{(-1)}^{5}\times {m}^{5}\times n^{2}}{(2\times {3}^{2})^{3}\times {m}^{3}\times n}$

$= \frac{(-1)\times{3}^{6}\times m^{5}\times n^{2}}{2^{3} \times3^{6}\times m^{3}\times n}$

$= \frac{(-1)\times \cancel{3 \times 3 \times 3 \times 3 \times 3 \times 3} \times \cancel{m \times m \times m} \times {m}^{2} \times \cancel{n} \times n}{ {2}^{3} \times\cancel{3 \times 3 \times 3 \times 3 \times 3 \times 3} \times \cancel{m \times m \times m} \times\cancel{n}}$

$= - {2}^{-3} {m}^{2} n$

$\underline{\text{Answer :}}$

$\boxed{\bold{- {2}^{-3}m^{2} n}}$

Answer 2

$\underline{\text{Answer :}}$

$Now, \frac{ {27}^{2} \times {( - m)}^{5} {n}^{2} }{ {18}^{3} \times {m}^{3}n} \\ \\ = - \frac{( { {3}^{3} )}^{2} \times {m}^{5} \times {n}^{2} }{ { {(3}^{2} \times 2)}^{3} \times {m}^{3} \times n } \\ \\ = - \frac{ \cancel{ {3}^{6}} \times {m}^{5} \times {n}^{2} }{ \cancel{ {3}^{6}} \times {2}^{3} \times {m}^{3} \times n} \\ \\ = - \frac{ {m}^{2} \times \cancel{ {m}^{3} } \times \cancel{ n} \times n}{ {2}^{3} \times \cancel{ {m}^{3}} \times \cancel{n } } \\ \\ = - \frac{ {m}^{2} n}{8}$

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