1. What is (10²)³?

(10²)³ represents the cube of the square of 10. It's a mathematical operation that first squares 10 (10×10) and then cubes the result (100×100×100).

2. Mathematical Explanation

The calculation follows these steps:

Or equivalently using exponent rules:

3. Exponent Rules Applied

Power of a Power Rule: \((a^m)^n = a^{m \times n}\)

This shows that raising a power to another power multiplies the exponents.

4. Practical Applications

Understanding exponent rules is fundamental in:

• Scientific notation calculations
• Computer science (binary, hexadecimal systems)
• Engineering calculations
• Financial compound interest formulas

5. Frequently Asked Questions (FAQ)

Q1: Why does (10²)³ equal 10⁶?
A: This demonstrates the exponent rule that when you raise a power to another power, you multiply the exponents.

Q2: What's the difference between (10²)³ and 10^(2³)?
A: (10²)³ = 10⁶ = 1,000,000 while 10^(2³) = 10⁸ = 100,000,000. The parentheses change the order of operations.

Q3: Can this rule be applied to any base?
A: Yes, the power of a power rule \((a^m)^n = a^{m \times n}\) works for any real number base a (except when a=0 and exponents are non-positive).

Q4: How is this related to scientific notation?
A: Scientific notation relies heavily on exponent rules for multiplication and division of very large or small numbers.

Q5: What's the practical significance of 10⁶?
A: 10⁶ represents one million and is used in measurements like:

• Megabytes (MB) in computing
• Micrometers (µm) in science
• Population counts in demographics