Question

Reduza a uma potência.
a) [(-2² )²] = 2⁴
b) 4/8 = 2³
c) 5². 5². 5¹ = 5⁶​

Answer 1

Explicação passo-a-passo:

1.

a) [(-2)^2]^2=(-2)^{2\cdot2}=(-2)^4[(−2)2]2=(−2)2⋅2=(−2)4

b) \dfrac{4}{8}=\dfrac{2^2}{2^3}=2^{2-3}=2^{-1}84=2322=22−3=2−1

c) 5^2\cdot5^5\cdot5^{-1}=5^{2+5-1}=5^{6}52⋅55⋅5−1=52+5−1=56

d) Veja que 4=2^24=22 e 8=2^38=23 . Assim:

4^3=(2^2)^3=2^{2\cdot3}=2^643=(22)3=22⋅3=26

Temos que:

2^2\cdot4^3\cdot8^1=2^2\cdot2^6\cdot2^3=2^{2+6+3}=2^{11}22⋅43⋅81=22⋅26⋅23=22+6+3=211

e) 10^2\cdot10^3\cdot10^4\cdot10^9=10^{2+3+4+9}=10^{18}102⋅103⋅104⋅109=102+3+4+9=1018

2.

\dfrac{2^2\cdot2^7\cdot2^1}{2^4\cdot2^3}=\dfrac{2^{2+7+1}}{2^{4+3}}=\dfrac{2^{10}}{2^7}=2^{10-7}=2^324⋅2322⋅27⋅21=24+322+7+1=27210=210−7=23