a) Seja [tex]\text{x}=(5,1)^{-2}=\left(\dfrac{51}{10}\right)^{-2}[/tex]
Temos que:
[tex]\text{x}=\left(\dfrac{51}{10}\right)^{-2}=\left(\dfrac{10}{51}\right)^2=\dfrac{100}{2~601}[/tex]
b) Analogamente, façamos [tex]\text{y}=(4,125)^{-1}=\left(\dfrac{4~125}{1~000}\right)^{-1}[/tex]
Logo:
[tex]\text{y}=\left(\dfrac{4~125}{1~000}\right)^{-1}=\dfrac{1~000}{4~125}[/tex]
c) Como antes, temos:
[tex]\text{w}=(0,25)^{-3}=\left(\dfrac{-25}{100}\right)^{-3}[/tex]
Desse modo:
[tex]\text{w}=\left(\dfrac{100}{-25}\right)^3=\dfrac{1~000~000}{-15~625}=-64[/tex]
d) Por fim, vemos que:
[tex]\text{z}=(-0,5)^{-1}=\left(\dfrac{-5}{10}\right)^{-1}=\dfrac{10}{-5}=-2[/tex]
