Question

Utilizando as propriedades da potenciação resolva as operações

a) (1/4)⁸ . (0,25)⁻⁵

b) 5 ^m⁻² : 5 ^m⁻¹

c) (1/2)¹° .16 / (1/4)²

d) 2 ^m⁺¹ .2^m⁺² . 4^m₋¹

Gente me ajuda pff

Answer 1

.
a)
$( \frac{1}{4} )^8\times(0,25)^{-5}= \\ \\ ( \frac{1}{4} )^8\times( \frac{25}{100} )^{-5}= \\ \\ ( \frac{1}{4} )^8\times( \frac{1}{4})^{-5}= \\ \\ ( \frac{1}{4} )^{8-5}=( \frac{1}{4} )^3$


b)
$5^{m-2}\div5^{m-1}= \\ \\ 5^{m-2-(m-1)}= \\ \\ 5^{\not m-2-\not m+1}=5^{-1}~~ou~~ \frac{1}{5}$


c)
$( \frac{1}{2})^{10}\times16\div( \frac{1}{4} )^2= \\ \\ 2^{-10}\times2^4\div4^{-2}= \\ \\ 2^{-10+4}\div(2^2)^2= \\ \\ 2^{-6}\div2^4= \\ \\ 2^{-6-4}=2^{-10}~~ou~~( \frac{1}{2} )^{10}$


d)
$2^{m+1}\times2^{m+2}\times4^{m-1}= \\ \\ 2^{m+1}\times2^{m+2}\times2^{2(m-1)}= \\ \\ 2^{m+1+m+\not2+2m-\not2}=2^{4m+1}$