%5E-1.jpeg "(2/5)^-1")
Understanding (2/5)^-1
In mathematics, a negative exponent signifies the reciprocal of the base raised to the positive version of the exponent. In this case, we have (2/5)^-1. Let's break it down:
The Reciprocal
The reciprocal of a number is simply 1 divided by that number. So, the reciprocal of (2/5) is:
1 / (2/5) = 5/2
The Exponent
The exponent -1 indicates that we need to raise the base to the power of 1.
Combining the Steps
Therefore, (2/5)^-1 is equivalent to:
(2/5)^-1 = 1 / (2/5)^1 = 1 / (2/5) = 5/2
Conclusion
In summary, (2/5)^-1 simplifies to 5/2. This demonstrates the principle of negative exponents as representing reciprocals.