For the first simplification we can use the rule for exponents:
#color(red)(a^0 = 1)#
#((2x^3color(red)(y^0)z)/(4xz^2))^5 > ((2x^3color(red)(1)z)/(4xz^2))^5 > ((2x^3z)/(4xz^2))^5#
Next simplification is to reduce the constants:
#((2x^3z)/(4xz^2))^5 > ((2x^3z)/((color(red)(2*2))xz^2))^5 >#
#((color(red)(cancel(color(black)(2)))x^3z)/((color(red)(cancel(2)*2))xz^2))^5 > ((x^3z)/(2xz^2))^5#
Next, we can take advantage of two other rules for exponents:

#color(blue)(x^a/x^b = x^(ab)#

#color(red)(x^a/x^b = 1/x^(ba)#
#((color(blue)(x^3)color(red)(z))/(2color(blue)(x)color(red)(z^2)))^5 > ((color(blue)(x^(31)))/(2color(red)(z^(21))))^5 > ((x^2)/(2z^1))^5#
Now, we can use yet another rule of exponents to further simplify this expression:
#color(red)((x^a)^b) = x^(a*b)#
#((x^2)/(2z^1))^5 > (x^(color(red)(2*5)))/(2^color(red)(5)z^color(red)(1*5)) > (x^10)/(32z^5)#