Question

$\frac{9n \times {3}^{5 \times ( {27)}^{3} } }{3 \times ( {81)}^{4} }$
find the value of n​

Answer 1

Step-by-step explanation:

$\large \frac{ {9}^{n} \times {3}^{5} \times {27}^{3} }{3 \times {81}^{4} } \\ \\ \large = \frac{ {( {3}^{2} )}^{n} \times {3}^{5} \times { ({3}^{3}) }^{3} }{ {3}^{1} \times { ({3}^{4}) }^{4} } \\ \\ \large = \frac{ {(3)}^{2 \times n} \times {3}^{5} \times {(3)}^{3 \times 3} }{ {3}^{1} \times {(3)}^{4 \times 4} } \\ \\ \large = \frac{ {3}^{2n} \times {3}^{5} \times {3}^{9} }{ {3}^{1} \times {3}^{16} } \\ \\ \large = \frac{ {3}^{2n} \times {(3)}^{5 + 9} }{ {(3)}^{1 + 16} } \\ \\ \large = \frac{ {3}^{2n} \times {3}^{14} }{ {3}^{17} } \\ \\ \large = \frac{ {3}^{2n} }{ {(3)}^{17 - 14} } \\ \\ \large = \frac{ {3}^{2n} }{ {3}^{3} } \\ \\ \large \boxed{ = \underline{ \underline{ \huge {(3)}^{2n - 3} }}}$