Simplifying expressions with radical exponents

Question

1. (243x^10y^5)^1/5

Could someone provide the answer to this problem along with explained steps to how you solved it please?

Answer 1

(243x^10y^5)^1/5

= (243^1/5)(x^10/5)(y^5/5

= fifth root of 243 time x^2y

= 3x^2y

243 has digits that sum to 9. that means it's divisible by 9 and 3

so 3 is the likely answer to what is the 5th root of 243, that would be a good guess without checking

fifth root of x^10 is x^2

fifth root of y^5 is y