Question

11) Descubra o valor de N para que a igualdade seja verdadeira(9³)-⁵:9-⁸=N
​

Answer 1

$N~=~\dfrac{\left(9^3\right)^{-5}}{9^{-8}}\\\\\\Aplicando~a~\underline{propriedade~da~potencia~de~potencia}\\\\\\N~=~\dfrac{9^{3\cdot(-5)}}{9^{-8}}\\\\\\N~=~\dfrac{9^{-15}}{9^{-8}}\\\\\\Aplicando~a~\underline{propriedade~do~quociente~de~potencias}\\\\\\N~=~9^{-15-(-8)}\\\\\\N~=~9^{-15+8}\\\\\\\boxed{N~=~9^{-7}}\\\\\\ou\\\\\\\boxed{N~=~\dfrac{1}{9^7}}$