Question

Reduza a expressão a uma só potência

Answer 1

Olá,

$\tt \: \dfrac{ {3}^{20} - {3}^{19} - {3}^{17} }{51} \\ \tt = \dfrac{ {3}^{17 + 3} - {3}^{17 + 2} - {3}^{17} }{3 \cdot17} \\ \tt \: = \dfrac{ {3}^{17} \cdot {3}^{3} - {3}^{17} \cdot {3}^{2} - {3}^{17} }{3 \cdot17} \\ \tt = \dfrac{ {3}^{17} \left( {3}^{3} - {3}^{2} - 1\right)}{3 \cdot17} \\ \tt = \dfrac{ {3}^{17} \left( 27 - 9 - 1\right)}{3 \cdot17} \\ \tt = \dfrac{ {3}^{17} \left( 17\right)}{3 \cdot17} \\ \tt = \dfrac{ {3}^{17} \cancel{\left( 17\right)}}{3 \cdot \cancel{17}} \\ \tt = \frac{ {3}^{17} }{3} \\ \tt = {3}^{17 - 1} \\ \tt = {3}^{16}$