%5E-2-without-exponents.jpeg "(9/5)^-2 Without Exponents")
Understanding (9/5)^-2 without Exponents
The expression (9/5)^-2 might seem intimidating at first glance, but it can be simplified without using exponents. Let's break it down step by step:
The Power of Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. In other words:
(a/b)^-n = (b/a)^n
Applying this to our problem, we get:
(9/5)^-2 = (5/9)^2
Simplifying the Expression
Now we have a much simpler expression: (5/9)^2. This means we need to multiply (5/9) by itself:
(5/9)^2 = (5/9) * (5/9)
To multiply fractions, we multiply the numerators and the denominators:
(5/9) * (5/9) = (5 * 5) / (9 * 9)
Finally, we simplify:
(5 * 5) / (9 * 9) = 25/81
Conclusion
Therefore, (9/5)^-2 is equivalent to 25/81 without using exponents. This demonstrates how understanding the rules of exponents can help simplify complex expressions.