%5E-2.jpeg "(9/4)^-2")
Understanding (9/4)^-2
This article explores the simplification of the expression (9/4)^-2. We'll delve into the properties of exponents and demonstrate how to arrive at the solution.
The Power of a Fraction Raised to a Negative Exponent
The expression involves two key concepts:
- Fractions: A fraction represents a part of a whole.
- Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent.
Simplifying the Expression
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Reciprocal: The negative exponent dictates that we take the reciprocal of the base. Therefore, (9/4)^-2 becomes (4/9)^2.
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Squaring the Fraction: We now need to square the fraction (4/9). This means multiplying the fraction by itself: (4/9) * (4/9) = 16/81.
The Final Result
Therefore, (9/4)^-2 simplifies to 16/81.
Key Takeaway
Understanding the properties of exponents, especially negative exponents, allows us to simplify complex expressions like (9/4)^-2. This process involves taking the reciprocal of the base and raising it to the positive value of the exponent.