(x^8 * y^4)^(1/10) + 3(x^(1/5) * y^(1/10) )^4
the exponent 1/10 on the left multiplies onto the x and y exponents like this
x^(8/10) * y^(4/10) + 3(x^(1/5) * y^(1/10) )^4
x^(4/5) * y^(4/10) + 3(x^(1/5) * y^(1/10) )^4
the exponent 4 on the right multiplies onto the y and exponents like this
x^(4/5) * y^(4/10) + 3(x^(4/5) * y^(4/10) )
you can combine the x^(4/5) * y^(4/10) like this
4(x^(4/5) * y^(4/10) )
you can only combine them like that because you have exactly the same thing x^(4/5) * y^(4/10) on the left and right sides