Simplifying (10^2)^3 as a Single Exponent
In mathematics, simplifying expressions is often crucial for understanding and manipulating them effectively. One common type of simplification involves combining exponents. Let's explore how to express (10^2)^3 as a single exponent.
Understanding the Rules of Exponents
To simplify this expression, we'll utilize two key rules of exponents:
 Power of a Power: (a^m)^n = a^(m*n)
 Negative Exponent: a^n = 1/a^n
Applying the Rules

Applying the Power of a Power Rule: (10^2)^3 = 10^(2*3)

Simplifying the Exponent: 10^(2*3) = 10^6

Applying the Negative Exponent Rule: 10^6 = 1/10^6
Therefore, (10^2)^3 can be simplified as a single exponent 1/10^6.
Key Takeaways
 By applying the appropriate exponent rules, we can effectively combine exponents and simplify complex expressions.
 Understanding the relationship between exponents and their reciprocals is essential for working with negative exponents.