if x^2=y^3, for what value of z does x^{3z}= y^9

if x^2=y^3, for what value of z does x^{3z}= y^9

y^9 = y^3 * y^3, so if we square the right side, we must square the left side for equivalence:
x^2 * x^2 = x^4

Therefore,
x^4 = y^9

Going back to our problem, x^{3z}= y^9, so 3z = 4

Divide each side by 3 to isolate z, and we have:
3z/3 = 4/3
z = 4/3