%5E-1.jpeg "(3/5)^-1")
Understanding (3/5)^-1
In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. Let's break down what (3/5)^-1 means and how to calculate it:
The Basics of Negative Exponents
- Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2 is 1/2.
- Negative Exponent Rule: x^-n = 1/x^n
Calculating (3/5)^-1
Applying the negative exponent rule, we can rewrite (3/5)^-1 as:
(3/5)^-1 = 1/(3/5)^1
Since any number raised to the power of 1 is itself, we have:
1/(3/5)^1 = 1/(3/5)
To divide by a fraction, we multiply by its reciprocal:
1/(3/5) = 1 * (5/3) = 5/3
Conclusion
Therefore, (3/5)^-1 is equivalent to 5/3.
This demonstrates that understanding negative exponents allows us to simplify seemingly complex expressions and arrive at a clear and concise result.