Question

1) Indique sob a forma de potência de 3:

(1/3) ⁻³ . (1/3) ² . (9³) ²

Answer 1

Explicação passo-a-passo:

Note que:

$\left(\dfrac{1}{3}\right)^{-3}=(3^{-1})^{-3}=3^{(-1)\cdot(-3)}=3^{3}$

$\left(\dfrac{1}{3}\right)^{2}=(3^{-1})^{2}=3^{(-1)\cdot2}=3^{-2}$

$(9^{3})^{2}=9^{3\cdot2}=9^{6}=(3^2)^{6}=3^{2\cdot6}=3^{12}$

Então:

$\left(\dfrac{1}{3}\right)^{-3}\cdot\left(\dfrac{1}{3}\right)^{2}\cdot(9^{3})^{2}=3^{3}\cdot3^{-2}\cdot3^{12}=3^{3-2+12}=3^{13}$