((1/2)8)^2

less than a minute read Jun 16, 2024

Solving ((1/2)⁸)²

This problem involves understanding the order of operations and how exponents work. Let's break it down step by step.

Understanding the Problem

We have a fraction raised to the power of 8, and then that result is raised to the power of 2. The order of operations dictates that we perform the operations within parentheses first, followed by exponents.

Step 1: Solving (1/2)⁸

(1/2)⁸ means multiplying (1/2) by itself 8 times.
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/256

Step 2: Solving (1/256)²

(1/256)² means multiplying (1/256) by itself.
(1/256) * (1/256) = 1/65536

Conclusion

Therefore, the solution to ((1/2)⁸)² is 1/65536.