Which expression is equivalent to root 2/cubed root 2

It's the second choice ⁶√2.

Step-by-step explanation:

Convert to fractional exponents:

√2 = 2^1/2

∛2 = 2^1/3

√2 / ∛2

= 2^1/2 / 2^1/3 = 2^(1/2-1/3)

= 2^(1/6)

Now change back to radicals:

= ⁶√2.

use an integrating factor

y' + xy = 138x

I F = e ∫ xdx = e ^(x^2/2)

y' e^(x^2/2) + xy e^x^2/2 = 138x e^x^2/2

x y * e^x2/2 = 138∫x e^x^2/2 dx

xy * e ^(x^2/2) = 138 e^(x^2/2)

y = 138/ x + c