%5E-2.jpeg "(1/9)^-2")
Understanding (1/9)^-2
The expression (1/9)^-2 might look intimidating, but it's actually quite simple to solve once we understand the rules of exponents.
The Basics of Exponents
An exponent indicates how many times a base number is multiplied by itself. For example, 2^3 means 2 * 2 * 2 = 8.
Negative Exponents
A negative exponent means the reciprocal of the base raised to the positive value of the exponent. In other words, x^-n = 1/x^n.
Applying the Rules
Let's break down (1/9)^-2:
- Negative exponent: We know that (1/9)^-2 is equivalent to 1/(1/9)^2.
- Simplify the denominator: (1/9)^2 means (1/9) * (1/9) = 1/81.
- Final Calculation: 1/(1/81) = 81.
Therefore, (1/9)^-2 = 81.
Key Takeaways
- A negative exponent indicates taking the reciprocal of the base raised to the positive value of the exponent.
- Understanding the rules of exponents is crucial for solving complex expressions.
- Applying the rules step by step helps break down the problem and find the solution.