8)%5E2-calculator.jpeg "((1/2)8)^2 Calculator")
Understanding the Calculation: ((1/2)⁸)²
This expression involves multiple operations: parentheses, exponents, and multiplication. Let's break it down step by step.
1. Calculate the innermost parentheses:
- (1/2)⁸: This means raising 1/2 to the power of 8.
- (1/2)⁸ = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/256
2. Calculate the outer exponent:
- (1/256)²: This means squaring the result from the previous step.
- (1/256)² = (1/256) * (1/256) = 1/65536
Therefore, ((1/2)⁸)² = 1/65536
Using a Calculator:
Most calculators will handle this calculation efficiently. Here's how you might input it:
- Parentheses: Make sure to use parentheses to ensure the correct order of operations.
- Exponent button: Look for a button that looks like "x^y" or "y^x" to raise a number to a power.
- Enter the expression: Enter the expression as: (1/2) ^ 8 ^ 2
The calculator should display the final result: 1/65536
Key Points to Remember:
- Order of operations: Always follow the order of operations (PEMDAS/BODMAS) to ensure correct calculations.
- Parentheses: Use parentheses to group calculations and clarify the order.
- Exponent button: Use the exponent button to raise numbers to a power.