Question

simplify the question

and send me photos solution
fast it's a challenge
​

Answer 1

Answer:

27/125

kindly check the attachment for the stepwise solution and answer.

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Answer 2

GIVEN :-

$\mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{9}{25} \bigg) ^{2} \times \bigg( \dfrac{ - 18}{125} \bigg) ^{0} }{ \dfrac{ - 27}{ 125} \times \bigg( \dfrac{ - 3}{5} \bigg)}$

TO FIND :-

$\mapsto \sf value \: of \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{9}{25} \bigg) ^{2} \times \bigg( \dfrac{ - 18}{125} \bigg) ^{0} }{ \dfrac{ - 27}{ 125} \times \bigg( \dfrac{ - 3}{5} \bigg)}$

SOLUTION :-

$\mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{9}{25} \bigg) ^{2} \times \bigg( \dfrac{ - 18}{125} \bigg) ^{0} }{ \dfrac{ - 27}{ 125} \times \bigg( \dfrac{ - 3}{5} \bigg)}$

• By using identity:- x⁰ = 1.

$\\ \mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{9}{25} \bigg) ^{2} \times 1 }{ \dfrac{ - 27}{ 125} \times \bigg( \dfrac{ - 3}{5} \bigg)} \\ \\ \\ \mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{9}{25} \bigg) ^{2} }{ \dfrac{ - 27}{ 125} \times \bigg( \dfrac{ - 3}{5} \bigg)} \\ \\ \\ \mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3} \times \bigg( \dfrac{3}{5} \bigg) ^{4}}{ \bigg(\dfrac{ - 3}{ 5 } \bigg) ^{3} \times \bigg( \dfrac{ - 3}{5} \bigg)}$

• By using identity:- x² ÷ x³ = x² - ³.

$\\ \mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{3 - 3} \times \bigg( \dfrac{3}{5} \bigg) ^{4}}{ \bigg( \dfrac{ - 3}{5} \bigg)} \\ \\ \\ \mapsto \sf \: \dfrac{ \bigg( \dfrac{ - 3}{5} \bigg) ^{0} \times \bigg( \dfrac{3}{5} \bigg) ^{4}}{ \bigg( \dfrac{ - 3}{5} \bigg)}$

• By using identity:- x⁰ = 1.

$\\ \mapsto \sf \: \dfrac{ 1 \times \bigg( \dfrac{3}{5} \bigg) ^{4}}{ \bigg( \dfrac{ - 3}{5} \bigg)} \\ \\ \\ \mapsto \sf \: { \dfrac{ \cancel3}{5} \times \dfrac{3}{5} \times \dfrac{3}{5} \times \dfrac{3}{ \cancel5} } \times \dfrac{ \cancel{- 5}}{ \cancel3} \\ \\ \\ \mapsto \underline{\boxed{ \red{ \sf \: \frac{ - 27}{125} }}}$

Hence the required answer is -27/125.

ADDITIONAL INFORMATION :-

$\boxed{\begin{minipage}{7cm} \\ \sf{ \implies \bf \sqrt[n]{ \sqrt[m]{ \sqrt[p]{((a^{x} )^{y}) ^{z} } } } = (a ^{xyz} )^{ \frac{1}{mnp} } = a ^{ \frac{xyz}{mnp} } } \\ \\ \sf{ \implies a^m \times a^n = a^{m+n} } \\ \\ \sf{ \implies {a}^{m} \times b^m = ab^m } \\ \\ \sf{ \implies \dfrac{a^m}{a^n} = a^{m - n} ( \tt{ If \: m > n} ) } \\ \\ \sf{ \implies \dfrac{a^m}{ a^n} = \dfrac{ 1}{ a^{n-m} } ( \tt{ If \: n > m )} } \\ \\ \sf{ \implies (a^m)^n = a^{mn} } \\ \\ \sf{ \implies a^{-n} = \dfrac{1}{ a^n} }\end{minipage}}$