Question

How do you simplify `(\frac { x ^ { 0} y ^ { 4} } { 2y x ^ { - 4} \cdot x ^ { 3} y ^ { 0} } ) ^ { 2}`?

Answer 1

`(x^2y^6)/4`

Explanation:

Given: `((x^0 y^4)/(2yx^-4*x^3y^0))^2`

We can see that `x^0 = y^0 = 1` and we know `x^-4*x^3 = x^-1`

because multiplying like unknowns allows us to add exponents.

Then:
`((x^0 y^4)/(2yx^-4*x^3y^0))^2 = (y^4/(2yx^-1))^2 = ((y^3)/(2/x))^2 = ((xy^3)/2)^2 = ((xy^3)/2) * ((xy^3)/2) = (x^2y^6)/4`