Question

please don't spam please tell answer​

Answer 1

Required Answer:-

Given to evaluate:

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

Solution:

We know that,

$\sf \implies {x}^{a} \times {x}^{b} = {x}^{a + b}$

Therefore,

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

$\sf = \bigg( \dfrac{ {x}^{3n + 1 + 3n - 1}}{ {x}^{2n + 1} } \bigg)^{2}$

$\sf = \bigg( \dfrac{ {x}^{6n}}{ {x}^{2n + 1} } \bigg)^{2}$

We know that,

$\sf \implies \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$

So,

$\sf \bigg( \dfrac{ {x}^{6n}}{ {x}^{2n + 1} } \bigg)^{2}$

$\sf = {( {x}^{6n - 2n - 1}) }^{2}$

$\sf = {( {x}^{4n - 1}) }^{2}$

$\sf = {x}^{2(4n - 1)}$

$\sf = {x}^{8n - 2}$

Hence, the final value is x⁸ⁿ/x²

Answer:

• The simplified form of the expression is x⁸ⁿ/x²

Answer 2

$\mathrm \red{Given : \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf{ {\Bigg( \frac{ {x}^{3n + 1} \: . \: {x}^{3n - 1} }{ {x}^{2n + 1} } \Bigg)}^{2} \: \: \: \: \: \: (x \cancel{ = }0) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf{ {\Bigg( \frac{{x}^{(3n + 1 + 3n - 1)} }{ {x}^{2n + 1} }\Bigg)}^{2} } \: \: \: \: \mathrm \green{\Big[ {a}^{m}. {a}^{n} \: = \: {a}^{(m + n)} \Big ]}$

$\mathsf{ = {\Bigg( \frac{{x}^{(3n + 1 + 3n - 1)} }{ {x}^{2n + 1} }\Bigg)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf{ = {\Big( {x}^{6n - (2n + 1)} \Big)}^{2} } \: \: \: \: \: \: \: \: \ \: \mathsf \green{\Bigg[ \frac{ {x}^{m} }{ { {x}^{n}} } = {x}^{m - n}\Bigg] \: \: \: \: \: \: \: \: \: \: \: \: \:}$

$\mathsf{ {= ({x}^{(6n - 2n - 1)})}^{2} } \\ \\ \mathsf{ = {({x}^{4n - 1 })}^{2} \: \: \: \: \: \: \: \: } \\ \\ \mathsf{ = \: {x}^{8n - 2} \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\mathsf{ =\Big( \frac{ {x}^{8n} }{ {x}^{2} } \Big) }$

$\\ \boxed { \therefore \: \: \: \: \mathsf \red{ {\Bigg( \frac{ {x}^{3n + 1} \: . \: {x}^{3n - 1} }{ {x}^{2n + 1} } \Bigg)}^{2}} \: \: \red{ =} \: \mathsf \red{\frac{ {x}^{8n} }{ {x}^{2}} } }$