Question

A) (a^2 . b^3)^2 . (a^3 . b^2)^3=

B) (a^4 . b^2)^3
_______ =
(a . b^2)^2

C) (a^4 . b^3) ^5
________ =
a^2 . b

D) 2^-1 - (-2)^2 + (-2)^-1
_______________ =
2^2 + 2^2
Preciso de ajuda!!!!!!

Answer 1

vamos lá....

a, b , c  aplicar as propriedades da potenciação

a)
$(a^2.b^3)^2.(a^3.b^2)^3= \\ a^4.b^6.a^9.b^6= \\ a^{4+9}.b^{6+6}= \\ a^{13}.b^{12}$

b)
$\frac{(a^4.b^2)^3}{(a.b^2)^2} = \frac{a^{12}.b^6}{a^2.b^4} =a^{12-2}.b^{6-4}=a^{10}.b^2$ 

c)
$\frac{(a^4.b^3)^5}{a^2.b} = \frac{a^{20}.b^{15}}{a^2.b} =a^{20-2}.b^{15-1}=a^{18}.b^{14}$

d)
$\frac{2^{-1}-(-2)^2+(-2)^{-1}}{2^2+2^2} = \\ \\ \frac{ \frac{1}{2}-(+4)+(- \frac{1}{2} ) }{4+4} = \\ \\ \frac{-\not \frac{1}{2}-4-\not \frac{1}{2} }{8} =- \frac{4}{8} =- \frac{1}{2}$