Question

Find δ and β such that

X^3/8 * y^-6/7 *[y^9/7 / X^45/8]^1/9 = X^δ/yβ

Answer 1

[y^9/7 / x^45/8]^1/9 = y^1/7 / x^5/8

So, now you just have
x^3/8 * y^-6/7 * y^1/7 * x^-5/8 = x^-1/4 * y^-5/7
...