Question

Simplifique as operações reduzindo-as a uma unica potencia:

a) π^-2 . π^-5
----------------------- =
π^-7


b) (π³) ^-2
------------------ =
π^-4


c) (π³ . π^5) ^2
----------------------- =
π^-2 . (π³)^5

Answer 1

vamos lá...

$a) ~~ \frac{ \pi ^{-2}. \pi ^{-5}}{ \pi ^{-7}} = \frac{ \pi ^{-2-5}}{ \pi ^{-7}} = \pi ^{-7}\div \pi ^{-7}= \pi ^{-7-(-7)}= \pi ^{-7+7}= \pi ^0=1 \\ \\ b)~~ \frac{( \pi^3)^{-2} }{ \pi^{-4}} = \frac{ \pi ^{-6}}{ \pi ^{-4}} = \pi ^{-6}\div \pi ^{-4}= \pi ^{-6-(-4)}= \pi ^{-6+4}= \pi ^{-2} \\ \\ c)~~ \frac{( \pi ^3. \pi ^5)^2}{ \pi ^{-2}.( \pi ^3)^5} = \frac{( \pi ^8)^2}{ \pi ^{-2}. \pi ^{15}} = \frac{ \pi ^{16}}{ \pi ^{13}} = \pi^{16-13}= \pi ^3$