Question

Simplifique a expressão

Answer 1

$\frac{7^{2a+3} \ - \ 49^{a}}{49^{a+1}} \\ \\ \frac{7^{2a+3} \ - \ (7^{2})^{a}}{(7^{2})^{(a + 1)}} \\ \\ \frac{7^{2a+3} \ - \ 7^{2a}}{7^{2a+2}}$

Dividindo:

$7^{(2a+3) - (2a+2)} \ - \ 7^{2a - (2a+2)} = \\ \\ 7^{2a + 3 - 2a - 2} \ - \ 7^{2a - 2a - 2} = \\ \\ 7^{1} \ - \ 7^{-2} = \\ \\ 7 - \frac{1}{7^{2}} = \\ \\ 7 - \frac{1}{49} = \\ \\ \frac{343 - 1}{49} = \frac{342}{49}$