The equation shown in the image is:

$y = \sqrt{(2x + 2)^4}$

We can simplify this expression step by step.

Simplification:

1. The square root and the exponent of 4 can be combined: $\sqrt{(2x + 2)^4} = (2x + 2)^2$ This is because $\sqrt{a^4} = a^2$.

2. Now expand $(2x + 2)^2$: $(2x + 2)^2 = (2x + 2)(2x + 2)$

3. Perform the multiplication: $(2x + 2)(2x + 2) = 4x^2 + 8x + 4$

Thus, the simplified expression for $y$ is: $y = 4x^2 + 8x + 4$

Let me know if you need further details on this simplification, or if you'd like me to assist you with any other problem!

Related Questions:

1. How would this expression change if the exponent were different, say $(2x + 2)^6$?
2. What is the derivative of the simplified function $y = 4x^2 + 8x + 4$?
3. How do you solve for $x$ when $y = 4x^2 + 8x + 4$?
4. Can you factor $y = 4x^2 + 8x + 4$?
5. How would you approach simplifying an expression with a cube root instead?

Tip:

Whenever you see a square root combined with an even exponent, it's often a hint that the expression can be simplified by reducing the exponent first.