Question

evaluate this question and write the answer ​

Answer 1

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• $\sf \implies\dfrac{ {x}^{5 + n }\times ( {x}^{2}) ^{3n + 1} }{ {x}^{7n - 2} }$

$\\\underline { \underline{\bf{\pink{\text{Answer=\bf\green{{x⁹}}}}}}}$

$\\\\ \underline{\bf{Step \: by \: step \: explanation}}$

$\\ \sf \implies\dfrac{ {x}^{5 + n }\times ( {x}^{2}) ^{3n + 1} }{ {x}^{7n - 2} }$

$\sf \implies\dfrac{ {x}^{5 + n }\times ( {x}^{(2 \times 3n )+ (2 \times 1)}) }{ {x}^{7n - 2} }$

$\sf \implies\dfrac{ {x}^{5 + n }\times {x}^{6n + 2} }{ {x}^{7n - 2} }$

$~~~~\sf \implies\dfrac{ {x}^{5 + n + 6n + 2} }{ {x}^{7n - 2} }$

$~~~~\sf \implies\dfrac{ {x}^{7n + 7} }{ {x}^{7n - 2} }$

$~~~~~{\sf \implies {x}^{7n + 7 - (7n - 2)} }$

$~~~~~~{\sf \implies {x}^{7n + 7 - 7n + 2} }$

$~~~~~~~\overbrace↑^{\underbrace{\underline{\boxed{\underline{\sf \implies \orange{{x}^{9}}}}}}}$

Laws of exponents

$~~~~\begin{gathered}\sf {a}^{m} \times {a}^{n} = {a}^{m + n} \: \: \: \: \: \: \: \: \: \: \sf {a}^{m} \div {a}^{n} = {a}^{m - n} \\ \sf{( {a}^{m} ) ^{n} = {a}^{mn} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a {}^{m} \times {n}^{m} = (ab) ^{m} } \\ \sf{a}^{0} = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\frac{ {a}^{m} }{ {b}^{m} }= \left( \frac{a}{b} \right) ^{m} }\\\\\end{gathered}$

Answer 2

Step-by-step explanation:

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