Question

2) calcule usando as propriedades da potenciação:

a) 4^2 x 4^5 x 4^-7 x 4^3 b) (3^2)^3
c) 2° x 2^3 x 2^1 x 2^-6 x 2^5
d) 3^3:3^3
e) (2/3)^3 . (2/3)^2
f) (2/5)^8 : (2/5)^3 : (2/5)^7
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Answer 1

a.

$4^2\cdot4^5\cdot4^{-7}\cdot4^3=4^{2+5-7+3}=4^3=64$

b.

$(3^2)^3=3^{2\cdot3}=3^6=729$

c.

$2^0\cdot2^3\cdot2^1\cdot2^{-6}\cdot2^5=2^{0+3+1-6+5}=2^3=8$

d.

$3^3:3^3=3^{3-3}=3^0=1$

e.

$(2/3)^3\cdot(2/3)^2=(2/3)^{3+2}=(2/3)^5=2^5/3^5=32/243$

f.

$(2/5)^8 : (2/5)^3 : (2/5)^7= (2/5)^{8-3-7}= (2/5)^{-2}= (5/2)^2=25/4$