Question

Simplify: $\frac{7^{2n+3}(49{)}^{n+2}}{\left(\right(343{)}^{n+1}{)}^{2/3}}$

Answer 1

$\frac{7^{2n+3}{49}^{n-2}}{{\left({343}^{n+1}\right)}^{\frac{2}{3}}}$

$=\frac{7^{2n+3}{\left(7^2\right)}^{n-2}}{{\left({\left(7^3\right)}^{n+1}\right)}^{\frac{2}{3}}}$

$=\frac{7^{2n+3}{7}^{2n-4}}{{\left(7^{3n+3}\right)}^{\frac{2}{3}}}$

$=\frac{7^{2n+3+2n-4}}{7^{2n+2}}$

$=\frac{7^{4n-1}}{7^{2n+2}}$

$=7^{4n-1-2n-2}$

$=7^{2n-3}$