Final answer:
To simplify the expression (y² * √(4)(x))³ * z⁰, we can apply the rules of exponents. The simplified expression is 8y⁶x√(x)³.
Step-by-step explanation:
To simplify the expression (y² * √(4)(x))³ * z⁰, we can apply the rules of exponents. First, let's simplify the term inside the parentheses:
y² * √(4)(x) = y² * 2√(x) = 2y²√(x)
Now, let's cube the entire expression:
(2y²√(x))³ = (2³)(y²³)(√(x)³) = 8y⁶√(x)³ = 8y⁶x√(x)³
Lastly, any number raised to the power of 0 is always equal to 1, so we can simplify z⁰ to just 1:
8y⁶x√(x)³ * z⁰ = 8y⁶x√(x)³ * 1 = 8y⁶x√(x)³ = 8y⁶x√(x)³