Question

Utilizando propriedades de potências, simplifique as expressões a seguir.​

Answer 1

Resposta:

a) $\frac{25}{5^{3}} = \frac{5^{2}}{5^{3}} = 5^{2} : 5^{3} = 5^{2 - 3} = 5^{-1}$

b) $2^{4} . 3^{4} . 6 = 2^{4} . 3^{4} . 2 . 3 = 2^{4 + 1} . 3^{4 + 1} = 2^{5} . 3^{5}$

c) $\frac{2^{3}.5}{10^{3}} = \frac{2^{3}.5}{(5.2)^{3}} = 2^{3}.5 : (5.2)^{3} = 2^{3}.5 : (5^{3}.2^{3}) = 2^{3-3}.5^{1-3} = 2^{0}.5^{-2} = 1.5^{-2}$

= $5^{-2}$

d) $(7^{6})^{2}.49^{-5}.(7^{2})^{3} = 7^{12}.(7^{2})^{-5}.7^{6} = 7^{12}.7^{-10}.7^{6} = 7^{12-10+6} = 7^{8}$