Explanation:
sqrt(80x⁴y⁹)
80 = 4×4×5
so, sqrt(80) = 4×sqrt(5)
sqrt(x⁴) = x²
sqrt(y⁹) is ugly. because 9 cannot be divided by 2 as integer result.
we could write it as
sqrt(y⁹) = y^9/2 = y^4.5
so, we either keep it under the square root or we need to do the ugly thing. what does your teacher want ?
so, the result could be either
4x²×sqrt(5y⁹)
a = 4x²
b = 5y⁹
or
4x²y^9/2 × sqrt(5)
a = 4x²y^9/2
b = 5
I personally find the first option the nicer simplification.