%5E-1.jpeg "(9/5)^-1")
Understanding (9/5)^-1
The expression (9/5)^-1 might seem intimidating at first glance, but it's actually quite simple to understand. Here's a breakdown of what it means and how to calculate it:
Negative Exponents
The key lies in the negative exponent. In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. In other words:
x^-n = 1/x^n
Applying the Concept
In our case, (9/5)^-1 is equivalent to:
(9/5)^-1 = 1 / (9/5)^1
Since any number raised to the power of 1 is itself, we have:
(9/5)^-1 = 1 / (9/5)
To divide by a fraction, we flip the fraction and multiply:
(9/5)^-1 = 1 * (5/9)
Therefore, (9/5)^-1 = 5/9.
In Conclusion
The expression (9/5)^-1 represents the reciprocal of the fraction 9/5. This is a fundamental concept in mathematics, and understanding it can help you work with exponents and fractions more effectively.