Question

Alguém me ajuda a resolver essa conta?
1- O resultado de $\frac{3^{-1} + 3^{-2}}{0,555...}$ é:

Rápido, por favor!!!!!

Answer 1

Expoente negativo

$\huge\boxed{\boxed{\mathtt{{(\dfrac{a}{b})}^{-n}={(\dfrac{b}{a})}^{n}}}}$

$\mathsf{{3}^{-1}=\dfrac{1}{3}}$

$\mathsf{{3}^{-2}={(\dfrac{1}{3})}^{2}=\dfrac{1}{9}}$

$\mathsf{0,555...=\dfrac{5}{9}}$

substituindo temos:

$\mathsf{\dfrac{{3}^{-1}+{3}^{-2}}{0,555...}}\\\mathsf{\dfrac{\frac{1}{3}+\frac{1}{9}}{\frac{5}{9}}}\\\\\mathsf{\dfrac{\frac{3+1}{9}}{\frac{5}{9}}}$

$\mathsf{\dfrac{\frac{4}{9}}{\frac{5}{9}}}\\\mathsf{\dfrac{4}{9}\times\dfrac{9}{5}}\\\\\huge\boxed{\boxed{\mathsf{\dfrac{4}{5}}}}}$