Question

Exercícios de potência.​

Answer 1

Explicação passo-a-passo:

a)

$\sf 2^3\cdot2^4\cdot2^6\cdot2^2=2^{3+4+6+2}=2^{15}$

b)

$\sf (6^3)^6=6^{3\cdot6}=6^{18}$

c)

$\sf \dfrac{6^7}{6^5}=6^{7-5}=6^2$

d)

$\sf (3^3)^4=3^{3\cdot4}=3^{12}$

e)

$\sf \dfrac{11^5}{11^3}=11^{5-3}=11^2$

f)

$\sf \left[\left(\dfrac{1}{2}\right)^2\right]^{-1}=\left(\dfrac{1}{2}\right)^{2\cdot(-1)}=\left(\dfrac{1}{2}\right)^{-2}$

g)

$\sf \left(\dfrac{1}{4}\div\dfrac{1}{2}\right)^{-3}$

$\sf =\left(\dfrac{2^{-2}}{2^{-1}}\right)^{-3}$

$\sf =[2^{-2-(-1)}]^{-3}$

$\sf =(2^{-2+1})^{-3}$

$\sf =(2^{-1})^{-3}$

$\sf =2^{(-1)\cdot(-3)}$

$\sf =2^{3}$

h)

$\sf (3\cdot4)^2=12^2$

i)

$\sf \left(\dfrac{2}{5}\right)^{-1}\cdot\left(\dfrac{2}{5}\right)^{3}=\left(\dfrac{2}{5}\right)^{-1+3}=\left(\dfrac{2}{5}\right)^{2}$