Final answer:
The simplified expression for (8x¹¹z⁰)² is 64x³¸, by raising each element inside the parentheses to the power of 2.
Step-by-step explanation:
The student is asking to simplify the mathematical expression (8x¹¹z⁰)². To simplify this expression, we need to apply the power of a product rule, which tells us to raise each factor inside the parentheses to the power outside the parentheses.
Since any number (other than zero) raised to the power of zero is one, z⁰ becomes 1. Then, raising 8 to the power of 2 gives us 64, and raising x¹¹ to the power of 2 gives us x³¸ (by multiplying the exponents). The resulting simplified expression is 64x³¸.