Question

Simplifique a expressão e dê a resposta utilizando expoente positivo:

7⁻¹a⁰b⁻²/(3ab)⁻⁴

Answer 1

$\textbf{Algumas informa\c{c}\~oes:}\\\\ \mathrm{\Rightarrow x^{-k}=\dfrac{1}{x^k}\ \ \bigg\|\ \ \Rightarrow x^0=1\ \ \bigg\|\ \ \Rightarrow \dfrac{m}{\frac{n}{p}}=m.\dfrac{p}{n}\ \ \bigg\| \ \ (xy)^k=x^k.y^k}$

$\textbf{Resolu\c{c}\~ao:}\\\\ \mathrm{\dfrac{7^{-1}.a^0.b^{-2}}{(3ab)^{-4}}=7^{-1}.1.b^{-2}.\dfrac{1}{(3ab)^{-4}}=\dfrac{1}{7}.\dfrac{1}{b^2}.\dfrac{1}{\frac{1}{(3ab)^4}}=}\\\\ \mathrm{=\dfrac{1}{7b^2}.3^4.a^4.b^4=\dfrac{81.a^4.b^4}{7b^2}=\boxed{\mathbf{\dfrac{81a^4b^2}{7}}}}$