1. Paloule, usando as propriedades a) 4^2 cdot 4^3 cdot 4^-7 cdot 4^3= b) 2^0 cdot 2^3 cdot 2^2 cdot 2^-6 cdot 2^6= c) 6^12: 6^3= d) 3^4 3^4= e) (3^2)^3= f((2)/(3))^2 cdot((2)/(3))^3= (a) ((1)/(2))^4((1)/(2))^6=

Vamos corrigir e detalhar as respostas:

a) $4^{2} \cdot 4^{3} \cdot 4^{-7} \cdot 4^{3} = 4^{2+3-7+3} = 4^{1} = 4$

b) $2^{0} \cdot 2^{3} \cdot 2^{2} \cdot 2^{-6} \cdot 2^{6} = 2^{0+3+2-6+6} = 2^{5} = 32$

c) $6^{12} : 6^{3} = 6^{12-3} = 6^{9}$

d) $3^{4} \cdot 3^{4} = 3^{4+4} = 3^{8}$

e) $\left(3^{2}\right)^{3} = 3^{2 \cdot 3} = 3^{6}$

f) $\left(\frac{2}{3}\right)^{2} \cdot \left(\frac{2}{3}\right)^{3} = \left(\frac{2}{3}\right)^{2+3} = \left(\frac{2}{3}\right)^{5} = \frac{32}{243}$

g) $\left(\frac{1}{2}\right)^{4} \cdot \left(\frac{1}{2}\right)^{6} = \left(\frac{1}{2}\right)^{4+6} = \left(\frac{1}{2}\right)^{10} = \frac{1}{1024}$

Portanto, as respostas corrigidas são:

a) 4
b) 32
c) $6^{9}$
d) $3^{8}$
e) $3^{6}$
f) $\frac{32}{243}$
g) $\frac{1}{1024}$