X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4

Varies directly means there is a constant k such that:
x = ky^(1/3)

When x = 1 and y = 27, we have:
27^1/3(k) = 1
3k = 1

To solve for k, we type in our equation into our search engine and we get:
k = 1/3

Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4:
4 = y^(1/3)/3

Cross multiply:
y^(1/3) = 4 * 3
y^(1/3) =12

Cube each side:
y^(1/3)^3 = 12^3
y = 1728