Question

1) Efetue as operações aplicando as propriedades estudadas:

a) 5 ⁻³ . 5⁻⁵ : 5⁻³
b) 16⁻³ : 2⁻¹ : 8⁻²
c) 4³ . 2³ : ( 8². 8⁻³)

Answer 1

Explicação passo-a-passo:

$\bullet~a^{m}\cdot a^{n}=a^{m+n}$

$\bullet~\dfrac{a^{m}}{a^{n}}=a^{m-n}$

a) $5^{-3}\cdot5^{-5}\div5^{-3}=5^{-3-5-(-3)}=5^{-3-5+3}=5^{-5}$

b) Veja que $16=2^4$, então $16^{-3}=(2^4)^{-3}=2^{4\cdot(-3)}^=2^{-12}$

Analogamente, $8=2^{3}$, de modo que, $8^{-2}=(2^3)^{-2}=2^{-6}$

Assim:

$16^{-3}\div2^{-1}\div8^{-2}=2^{-12}\div2^{-1}\div2^{-6}=2^{-12+1+6}=2^{-5}$

c) Temos que:

$4^{3}=(2^2)^{3}=2^{6}$

$8^{2}=(2^3)^{2}=2^6$

$8^{-3}=(2^3)^{-3}=2^{-9}$

Logo:

$4^3\cdot2^{3}\div(8^2\cdot8^{-3})=2^{6}\cdot2^{3}\div(2^{6}\cdot2^{-9})$

$=2^{6+3}\div2^{6-9}=2^{9}\div2^{-3}$

$=2^{9-(-3)}=2^{9+3}=2^{12}$