Question

Help this is due today

Answer 1

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.