Question

Aplique as propriedades adequadas e simplifique as expressões abaixo. '-'

Answer 1

a)

$E~=~x^5~.~x^2\\\\\\E~=~x^{\,5+2}\\\\\\\boxed{E~=~x^{7}}$

b)

$E~=~\frac{x^5}{x^2}\\\\\\E~=~x^{\,5-2}\\\\\\\boxed{E~=~x^3}$

c)

$E~=~\frac{a^3~.~a^{-4}~.~a^{7}}{a^9~.~a^{-8}}\\\\\\E~=~\frac{\,a^{3+(-4)+7}}{a^{\,9+(-8)}}\\\\\\E~=~\frac{a^{6}}{a^{1}}\\\\\\E~=~a^{\,6-1}\\\\\\\boxed{E~=~a^5}$

d)

$E~=~\left[\left(5^2~.~5^3\right)^2\right]^{-3}\\\\\\E~=~\left[\left(5^{\,2+3}\right)^2\right]^{-3}\\\\\\E~=~\left[\left(5^5\right)^2\right]^{-3}\\\\\\E~=~\left[5^{\,5~.~2}\right]^{-3}\\\\\\E~=~\left[5^{10}\right]^{-3}\\\\\\E~=~5^{\,10~.~(-3)}\\\\\\\boxed{E~=~5^{-30}}~~~~ou~~~~\boxed{E~=~\frac{1}{5^{30}}}$

e)

$E~=~\left[\frac{(2,5)^2~.~(2,5)^5~.~(2,5)^{25}}{(2,5)^{35}}\right]^{-4}\\\\\\E~=~\left[\frac{(2,5)^{\,2+5+25}}{(2,5)^{35}}\right]^{-4}\\\\\\E~=~\left[\frac{(2,5)^{32}}{(2,5)^{35}}\right]^{-4}\\\\\\E~=~\left[(2,5)^{\,32-35}\right]^{-4}\\\\\\E~=~\left[(2,5)^{-3}\right]^{-4}\\\\\\E~=~(2,5)^{\,-3~.~(-4)}\\\\\\\boxed{E~=~(2,5)^{12}}$