Mathematics

Problem

For positive real numbers

y

and

z

, the following statements are true: (i)

y^{5}=32

(ii)

(3z)^{3}=216

(a) Find the value of

y

. (b) Determine the value of

z

. (c) Using the results of parts (a) and (b), compute

E=y^{2}+z^{2}