Question

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Answer 1

Step-by-step explanation:

$\pink{ \clubsuit \: \mathfrak{ \underline{Question : }}}$

$\displaystyle{ \tt{ \blue{ \circ \: \frac{ {( {3}^{ - 2} )}^{2} \times ( {5}^{2} ) {}^{ - 3} \times ( {t}^{ - 3} ) {}^{2} }{( {3}^{ - 2} ) {}^{3} \times (5) {}^{ - 3} \times ( {t}^{ - 4}) {}^{3} } }}}$

$\: \:$

$\pink{ \clubsuit \: \mathfrak{ \underline{Solution : }}}$

As we know that,

$\sf{ {(a}^{m}){}^{n} = {a}^{mn} }$

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Let's start solving!

$\displaystyle{ \tt{ \leadsto \: \frac{ {3}^{ - 2 \times 2} \times {5}^{2 \times - 3} \times {t}^{ - 3 \times 2} }{ {3}^{ - 2 \times 3} \times {5}^{ - 3} \times {t}^{ - 4 \times 3} } }}$

$\displaystyle{ \tt{ \leadsto \: \frac{ {3}^{ - 4} \times {5}^{ - 6} \times {t}^{ - 6} }{ {3}^{ - 6} \times {5}^{ - 3} \times {t}^{ - 12} } }}$

$\: \:$

As we know that ,

$\sf{ {a}^{m} \div {a}^{n} = {a}^{m - n} }$

$\displaystyle{ \tt{ \leadsto \: {3}^{( - 4) - ( - 6)} \times {5}^{( - 6) - ( - 3)} \times {t}^{( - 6) - ( - 12)} }}$

$\displaystyle{ \tt{ \leadsto \: {3}^{ - 4 + 6} \times {5}^{ - 6 + 3} \times {t}^{ - 6 + 12} }}$

$\displaystyle{ \tt{ \leadsto \: {3}^{2} \times {5}^{ - 3} \times {t}^{6} }}$

$\underline{ \therefore \sf{The \: required \: answer \: is \: \pink{ {3}^{4} \times {5}^{ - 3} \times {t}^{6} .}}}$

$\: \:$

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$\pink{ \clubsuit \: \mathfrak{ \underline{More \: Information : }}}$

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$