Question

Simplify:[(27^n+2) -6.3^3n+3]÷9^n+2 *3^n​

Answer 1

Step-by-step explanation:

$[( {27})^{n + 2} - 6 \times {3}^{3n + 3} ] \div {9}^{n + 2} \times {3}^{n} \\ \\ = [( {3}^{3}) ^{n + 2} - 2 \times 3 \times {3}^{3n + 3} ] \div {( {3}^{2}) }^{n + 2} \times {3}^{n} \\ \\ = [ {3} ^{3n + 6} - 2 \times {3}^{3n + 4} ] \div {{3}}^{2n + 4} \times {3}^{n} \\ \\ = [ {3} ^{3n + 4} ( {3}^{2} - 2 ) ] \div {{3}}^{3n + 4} \\ \\ = \frac{ {3} ^{3n + 4} (9- 2 ) }{{{3}}^{3n + 4} } \\ \\ = 7$