[tex]{ \frak{ \longrightarrow \: \frac{3 \times {(27)}^{n + 1} + 9 \times {3}^{3n - 1} }{8 \times {3}^{3n} - 5 \times {(27)}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {(3 \times 3 \times 3)}^{n + 1} + (3 \times 3)\times {3}^{3n - 1} }{(2 \times 2 \times 2) \times {3}^{3n} - 5 \times {(3 \times 3 \times 3)}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {( {3}^{3} )}^{n + 1} + ( {3}^{2} )\times {3}^{3n - 1} }{( {2}^{3} ) \times {3}^{3n} - 5 \times {( {3}^{3} )}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {3}^{3(n + 1)} + {3}^{2} \times {3}^{3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {3}^{3n + 3} + {3}^{2} \times {3}^{3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{1 + 3n + 3} + {3}^{2 + 3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{ 3n + 4} + {3}^{3n + 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{ 3n + 4 - 3n} + {3}^{3n + 1 - 3n} }{{2}^{3} - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{4} + {3}^{1} }{2 \times 2 \times 2 - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times 3 \times 3 \times 3 + 3 }{8 - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{81 + 3 }{3 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{84 }{3 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: 28 }} \\ [/tex]
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[tex]\large \sf \hookrightarrow \: {a}^{m} \times {a}^{n} = {a}^{m + n}[/tex]
[tex]\large\sf \hookrightarrow \: {({a}^{m} ) }^{n} = {a}^{m \times n}[/tex]
[tex]\large\sf \hookrightarrow \: \frac{ { a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ [/tex]
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QuestioN:-
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {(27)}^{n + 1} + 9 \times {3}^{3n - 1} }{8 \times {3}^{3n} - 5 \times {(27)}^{n} } }} \\ [/tex]
SolutioN:-
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {(27)}^{n + 1} + 9 \times {3}^{3n - 1} }{8 \times {3}^{3n} - 5 \times {(27)}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {(3 \times 3 \times 3)}^{n + 1} + (3 \times 3)\times {3}^{3n - 1} }{(2 \times 2 \times 2) \times {3}^{3n} - 5 \times {(3 \times 3 \times 3)}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {( {3}^{3} )}^{n + 1} + ( {3}^{2} )\times {3}^{3n - 1} }{( {2}^{3} ) \times {3}^{3n} - 5 \times {( {3}^{3} )}^{n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {3}^{3(n + 1)} + {3}^{2} \times {3}^{3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times {3}^{3n + 3} + {3}^{2} \times {3}^{3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{1 + 3n + 3} + {3}^{2 + 3n - 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{ 3n + 4} + {3}^{3n + 1} }{{2}^{3} \times {3}^{3n} - 5 \times { 3}^{3n} } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{ 3n + 4 - 3n} + {3}^{3n + 1 - 3n} }{{2}^{3} - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{ {3}^{4} + {3}^{1} }{2 \times 2 \times 2 - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{3 \times 3 \times 3 \times 3 + 3 }{8 - 5 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{81 + 3 }{3 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: \frac{84 }{3 } }} \\ [/tex]
[tex]{ \frak{ \longrightarrow \: 28 }} \\ [/tex]
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Identities Used:-
[tex]\large \sf \hookrightarrow \: {a}^{m} \times {a}^{n} = {a}^{m + n}[/tex]
[tex]\large\sf \hookrightarrow \: {({a}^{m} ) }^{n} = {a}^{m \times n}[/tex]
[tex]\large\sf \hookrightarrow \: \frac{ { a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ [/tex]