Question

simplify the following with explanation
$\frac{ {3}^{n} \times {9}^{n + 1} }{ {3}^{n - 1} \times {9}^{n - 1} }$
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Answer 1

Step-by-step explanation:

$\frac{ {3}^{n} \times {9}^{n + 1} }{ {3}^{n - 1} \times {9}^{n - 1} } \\ = \frac{ {3}^{n} \times {3}^{2(n + 1)} }{ {3}^{n - 1} \times {3}^{2(n - 1)} } \\ = {3}^{n + 2n + 2} \div {3}^{n - 1 + 2n - 2} \\ = {3}^{3n + 2} \div {3}^{3n - 3} \\ = {3}^{3n + 2 - 3n + 3} \\ = {3}^{5}$