Question

Deixe a resolução por favor (e se puder o passo a passo), agradecimento adiantado!

Answer 1

Propriedades:

$x^{a}\cdot x^{b}=x^{a+b}\\\\\\\dfrac{x^{a}}{x^{b}}=x^{a-b}\\\\\\(x^{a})^{b}=x^{(a\cdot b)}$
________________________

$\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=\dfrac{(3^{2})^{3}\cdot3^{-2}}{3^{3}\cdot(3^{3})^{4}}\\\\\\\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=\dfrac{3^{6}\cdot3^{-2}}{3^{3}\cdot3^{12}}\\\\\\\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=\dfrac{3^{6-2}}{3^{3+12}}\\\\\\\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=\dfrac{3^{4}}{3^{15}}\\\\\\\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=3^{4-15}\\\\\\\boxed{\boxed{\dfrac{9^{3}\cdot3^{-2}}{3^{3}\cdot27^{4}}=3^{-11}}}$