Question

simplify this question please this is urgent ​

Answer 1

━━━━━━━━━━━━━━━━━━━━

$\huge{ \sf{ \underline{ \underline{ \purple{Answer...}}}}}$

♦️To Simplify:

• $\large{ \sf{[( \frac{3}{4}) {}^{ - 2} \div ( \frac{4}{5}) } {}^{ - 3} ] \times ( \frac{3}{5}) {}^{ - 2} }$

━━━━━━━━━━━━━━━━━━━━

$\huge{ \sf{ \underline{ \underline{ \purple{Concept \: used...}}}}}$

The above question is asking to simplify a exponential sum which can be done by using the different laws of exponents. The important laws of exponents are:-

$\large{ \sf{ \odot \: \: { {a}^{m} \times {a}^{n} = {a}^{m + n} }}} \\ \\ \large{ \sf{ \odot \: \: { \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }}} \\ \\ \large{ \sf{ \odot \: \: {( \frac {a} {b}) {}^{m} = \frac{ {a}^{m} }{ {b}^{m} } }}} \\ \\ \large{ \sf{ \odot \: \: { {a}^{ - m} = \frac{1}{ {a}^{m} }}}} \\ \\ \large{ \sf{ \odot \: \: {( \frac{a}{b}) {}^{ - m} = ( \frac{b}{a}) {}^{m} }}}$

﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏﹏ ✍

↪ More formulas:

$\large{ \sf{ \odot \: \: {(ab) {}^{m} = {a}^{m} {b}^{m} }}} \\ \\ \large{ \sf{ \odot \: \: {( {a}^{m}) {}^{n} = (a) {}^{mn} }}} \\ \\ \large{ \sf{ \odot \: \: { {a}^{0} = 1}}} \\ \\ \large{ \sf{ \odot \: \: { {a}^{1} = a}}}$

By using these laws, we can solve the given question.

━━━━━━━━━━━━━━━━━━━━

$\huge{ \sf{ \underline{ \underline{ \purple{Solution...}}}}}$

By using the laws of exponents listed above,

$\large{ \sf{ \rightarrow{[( \frac{3}{4}) {}^{ - 2} \div ( \frac{4}{5}) } {}^{ - 3} ] \times ( \frac{3}{5}) {}^{ - 2} }} \\ \\ \large{ \sf{ \rightarrow[( \frac{4}{3}) {}^{ 2} \div ( \frac{5}{4}) } {}^{ 3} ] \times ( \frac{5}{3}) {}^{ 2} } \\ \\ \sf{ \dag \: { \red{ by \: using \: (a {}^{ - m} = \frac{1}{ {a}^{m} }) }}} \\ \\ \large{ \sf{ \rightarrow[ \frac{4 {}^{2} }{3 {}^{2} } {} \div \frac{5 {}^{3} }{4 {}^{3} } } ] \times \frac{5 {}^{2} }{3 {}^{2} } } \\ \\ \sf{ \dag \: { \red{by \: using \: ( \frac{a}{b}) {}^{m} = \frac{a {}^{m} }{ {b}^{m} }}}} \\ \\ \large{ \sf{ \rightarrow[ \frac{4 {}^{2} }{3 {}^{2} } {} \times \frac{4 {}^{3} }{5 {}^{3} } } ] \times \frac{5 {}^{2} }{3 {}^{2} }} \\ \\ \large{ \sf{ \rightarrow \frac{4 {}^{2} }{3 {}^{2} } {} \times \frac{4{}^{3} }{5{}^{3} } } \times \frac{5 {}^{2} }{3 {}^{2} } } \\ \\ \large{ \sf{ \rightarrow \: \frac{ {4 {}^{2} \times {4}^{3} \times {5}^{2} } }{ {3}^{2} \times {3}^{2} \times {5}^{3} }}}$

By simplifying further,

$\large{ \sf{ \rightarrow \: {4}^{2} \times {4}^{3} \times {5}^{2} \times {5}^{ - 3} \times {3}^{ - 2} \times {3}^{ - 2} }} \\ \\ \large{ \sf{ \rightarrow \: {4}^{2 + 3} \times {5}^{2 + ( - 3)} \times {3}^{( - 2) + ( - 2)} }} \\ \\ \sf{ \dag{ \red{by \: using \: {a}^{m} \times {a}^{n} = {a}^{m + n} }}} \\ \\ \large{ \sf{ \rightarrow \: {4}^{5} \times {5}^{ - 1} \times 3 {}^{ - 4}}} \\ \\ \large{ \sf{ \rightarrow \: \frac{ {4}^{5} }{5 \times {3}^{4} }}} \\ \\ \large{ \sf{ \rightarrow \boxed{ \sf{ \green{\: \frac{1024}{405}}} (ans)}}}$

✍ Hence, simplified!!

━━━━━━━━━━━━━━━━━━━━