Question

Qual o valor da seguinte expressão na base 3

olhem a foto

a)
${3}^{11}$
b)
${3}^{? - 11}$
c)
${3}^{15}$
d)
${3}^{16}$
e)
${3}^{33}$

Answer 1

$\frac{9^3\;.\;3^{-2}}{3^3\;.\;27^4}\\\\\frac{(3^2)^3\;.\;3^{-2}}{3^3\;.\;(3^3)^4}\\\\\frac{(3)^{2\;.\;3}\;.\;3^{-2}}{3^3\;.\;(3)^{3\;.\;4}}\\\\\frac{(3)^{6}\;.\;3^{-2}}{3^3\;.\;(3)^{12}}\\\\\frac{3^{6+(-2)}}{3^{3+12}}\\\\\frac{3^{4}}{3^{15}}\\\\3^{4-15}\\\\3^{-11}$