Question

Aplicando as propriedades das potencias simplifique as expressões

A) 256.4⁹÷8⁷

B) 125⁶ x 25⁻³ ÷ (5²)⁻³ x 25⁷

C) 12 x 10⁻³ x 10⁻⁴ x 10⁻⁹ ÷ 3 x 10⁻¹ x 10⁴

Answer 1

Olá!

    a) $256 \cdot 4^9 \div 8^7=\dfrac{2^8 \cdot (2^2)^9}{(2^3)^7}= \dfrac{2^8 \cdot 2^{18}}{2^{21}}=\dfrac{2^{26}}{2^{21}}= \\ \\ =2^{(26-21)}=2^5=32$

    b) $125^6 \cdot 25^{-3} \div (5^2)^{-3} \cdot 25^7 = (5^3)^6 \cdot [(5^2)^{-3} \div (5^2)^{-3}] \cdot (5^2)^7 = \\ \\ = 5^{18} \cdot 1 \cdot 5^{14} = 5^{(18+14)}=5^{32}$


    c) 

$12 \cdot 10^{-3} \cdot 10^{-4} \cdot 10^{-9} \div 3 \cdot 10^{-1} \cdot 10^4= \\ \\ = 12 \cdot 10^{(-3-4-9)} \div 3 \cdot 10^{(-1+4)}=12 \cdot 10^{-16} \div 3 \cdot 10^3 = \\ \\ =\dfrac{12 \cdot 10^{-16}}{3 \cdot 10^3} = \dfrac{12}{3} \cdot \dfrac{10^{-16}}{10^3}=4 \cdot 10^{(-16-3)}=4 \cdot 10^{-19}$