How do i solve (x^8y^4)^1/10+3(x^1/5y^1/10)^4

Question

I want to know how to solve it, not just the answer

Answer 1

(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