Answer:
n = 3.
Step-by-step explanation:
nth root(54 . x^6 . y^ 12) = 3 x^2 y^4 nth root of 2
(54 . x^6 . y^ 12)^1/n = 3 x^2 y^4 2^1/n
54^1/n . (x^6)^1/n . (y^12)^1/n = 3 x^2 y^4 2^1/n
Consider the terms in x:
(x^6)^1/n = x^2
x^6/n = x^2
Therefore 6/n = 2 and n = 3.
Check this out with the constants in the expressions:
54 ^ 1/n = 3 * 2^1/n
54 ^ 1/3 = 27^1/3 * 2^1/3 = 3 * 2 1/3
- Checks OK.
