%5E-3-as-a-single-exponent.jpeg "(10^2)^-3 As A Single Exponent")
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
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Applying the Power of a Power Rule: (10^2)^-3 = 10^(2*-3)
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Simplifying the Exponent: 10^(2*-3) = 10^-6
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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.