The initial expresiion is:
[tex]x^y=z[/tex]Part A: If x = 3 and y = 4 then:
[tex]\begin{gathered} 3^4=z \\ 81=z \end{gathered}[/tex]Part B: is y = 3 and z = 125 then:
[tex]\begin{gathered} x^3=125 \\ x=\sqrt[3]{125} \\ x=5 \end{gathered}[/tex]Part C: if he rewrite the equation as:
[tex]\sqrt[y]{z}=x[/tex]and y = 2 and z = 2
then x will be a rational number because z is positive and the square root of a positive number is a rational number.
Part D: If x=8 then we can give the easier value to y so let it be y = 2 then we need to find a number that the square root is equal to 8 and this number is z = 64 so:
[tex]\sqrt[2]{64}=8[/tex]