Propostos 316 Utilize as propriedades adequadas a cada caso: a) 3^2cdot 3^3 3 b) 5^1cdot 5^-3=5^16-25=5 C) 2^-2cdot 2^-3 d) (2cdot 7)^2 e ((1)/(4)cdot (1)/(3))^2 f) (11^6:11^3)^2 317 Simplifique utilizando as propriedades: a) (5^2)^2 d) 4^6:4^2 b) (3^3)^-2 e) 3^2:3^-3 C) (0,2^-2)^-4 f) 7^-2:(7^-3)^2 318 Calcule, utilizando as propriedades: a) 0,2^-8:0,2^-6 d) (sqrt [3](5))^-3 b) ((1)/(3))^5 e) (10^-2cdot 10^-3)/(10^-2) C) ((5)/(4))^3 f) ((sqrt (pi ))/(2^0)cdot (1)/(2))^-2

316<br />a) $3^{2}\cdot 3^{3} = 3^{2+3} = 3^{5}$<br /><br />b) $5^{1}\cdot 5^{-3} = 5^{1-3} = 5^{-2}$<br /><br />c) $2^{-2}\cdot 2^{-3} = 2^{-2-3} = 2^{-5}$<br /><br />d) $(2\cdot 7)^{2} = 14^{2}$<br /><br />e) $(\frac {1}{4}\cdot \frac {1}{3})^{2} = (\frac {1}{12})^{2} = \frac {1}{144}$<br /><br />f) $(11^{6}:11^{3})^{2} = (11^{6-3})^{2} = 11^{6}$<br /><br />317<br />a) $(5^{2})^{2} = 5^{2\cdot 2} = 5^{4}$<br /><br />b) $(3^{3})^{-2} = 3^{3\cdot -2} = 3^{-6}$<br /><br />c) $(0,2^{-2})^{-4} = (0,2^{-2\cdot -4}) = 0,2^{8}$<br /><br />d) $4^{6}:4^{2} = 4^{6-2} = 4^{4}$<br /><br />e) $3^{2}:3^{-3} = 3^{2-(-3)} = 3^{5}$<br /><br />f) $7^{-2}:(7^{-3})^{2} = 7^{-2-(-3\cdot 2)} = 7^{-2}$<br /><br />318<br />a) $0,2^{-8}:0,2^{-6} = 0,2^{-8-(-6)} = 0,2^{-2}$<br /><br />b) $(\frac {1}{3})^{5} = \frac {1}{3^{5}} = \frac {1}{243}$<br /><br />c) $(\frac {5}{4})^{3} = \frac {5^{3}}{4^{3}} = \frac {125}{64}$<br /><br />d) $(\sqrt [3]{5})^{-3} = 5^{-1} = \frac {1}{5}$<br /><br />e) $\frac {10^{-2}\cdot 10^{-3}}{10^{-2}} = 10^{-2-3+2} = 10^{-3}$<br /><br />f) $(\frac {\sqrt {\pi }}{2^{0}\cdot \frac {1}{2}})^{-2} = (\frac {\sqrt {\pi }}{1\cdot \frac {1}{2}})^{-2} = (\sqrt {\pi }\cdot 2)^{-2} = (\sqrt {2\pi})^{-2} = \frac {1}{(\sqrt {2\pi})^{2}} = \frac {1}{2\pi}$