Question

Simplify 3^2(n+6)*(9)^2n-7/(27)^2n​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ {(3)}^{2(n + 6)} \times {(9)}^{2n - 7} }{ {(27)}^{2n} } }$

EVALUATION

$\displaystyle \sf{ \frac{ {(3)}^{2(n + 6)} \times {(9)}^{2n - 7} }{ {(27)}^{2n} } }$

$\displaystyle \sf{ = \frac{ {(3)}^{2n + 12} \times {( {3}^{2} )}^{2n - 7} }{ {( {3}^{3} )}^{2n} } }$

$\displaystyle \sf{ = \frac{ {(3)}^{2n + 12} \times {( 3 )}^{4n - 14} }{ {(3 )}^{6n} } }$

$\displaystyle \sf{ = \frac{ {(3)}^{2n + 12 + 4n - 14}}{ {(3 )}^{6n} } }$

$\displaystyle \sf{ = \frac{ {(3)}^{6n - 2}}{ {(3 )}^{6n} } }$

$\displaystyle \sf{ = {(3)}^{6n - 2 - 6n}}$

$\displaystyle \sf{ = {(3)}^{ - 2 }}$

$\displaystyle \sf{ = \frac{1}{ {3}^{2} } }$

$\displaystyle \sf{ = \frac{1}{ 9} }$

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Answer 2

Answer:

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