Question

Calcule as propriedades das potências.


obs- com passo a passo


a) $(-2)^6 * (-2)^5 * (-2)^-^8$



b) $(-5)^3 / (-5)^-^4$



c) [tex](\frac{1}{3} )[(8)^5]^5[tex]



d) [tex][(8)^5]^5

Answer 1

Resposta:

a)

$(-2)^{6}(-2)^{5}(-2)^{-8}=(-2)^{(6+5-8)}=(-2)^{3}=[(-1)(2)]^{3}=(-1)^{3}(2)^{3}=-8$

b)

$\frac{(-5)^{3}}{(-5)^{-4}}=(-5)^{3}(-5)^{4}=(-5)^{(3+4)}=(-5)^{7}=[(-1)(7)]^{7}=(-1)^{7}7^{7}=-823~543$

c)

$(\frac{1}{3} )[(8)^5]^5=(\frac{[(8)^5]^5}{3})=\frac{8^{(5*5)}}{3}=\frac{8^{25}}{3}$

d)

$[(8)^5]^5=8^{5*5}=8^{25}$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$