Verified answer

∜(x^4 y^5 z^6 ) =

(x^4 y^5 z^6)^(1/4) =

(x^4)^(1/4) (y^5)^(1/4) (z^6)^(1/4)

|x| y^(5/4) |z|^(6/4) =

|x| y^(5/4) |z|^(3/2)

Taking a root of a number (or variable in this case) is the same as raising it to the 1/root.

So the 4th root of x^4y^5z^6 = x^(4/4)y^(5/4)z^(6/4) = x^1y^(5/4)z^(3/2) = xy^(5/4)z^(3/2)

Hope this helps!

∜(x^4 y^5 z^6 )

can be rewritten

(x^4 y^5 z^6 ) ^ (1/4)

now separate each one

{ (x^4) * (y^5) * (z^6 ) } ^ (1/4)

and give each one the outside exponent

{ (x^4) ^ (1/4) } * { (y^5) ^ (1/4) } * { (z^6 ) ^ (1/4) }

and reduce

(x) * { y ^ (5/4) } * { z ^ (3/2) }

(x^4y^5z^6)^(1/4)

xy^(5/4)z^(3/2)

The fractional power postulate.