%5E-1.jpeg "(7/8)^-1")
Understanding (7/8)^-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 this means for (7/8)^-1:
Reciprocals
The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 5 is 1/5.
Applying the Rule
Applying the rule of negative exponents to (7/8)^-1, we get:
(7/8)^-1 = 1 / (7/8)^1
Since any number raised to the power of 1 is itself, we have:
1 / (7/8)^1 = 1 / (7/8)
Calculating the Result
To divide by a fraction, we multiply by its reciprocal. The reciprocal of (7/8) is (8/7). Therefore:
1 / (7/8) = 1 * (8/7) = 8/7
Conclusion
Therefore, (7/8)^-1 is equal to 8/7. This demonstrates how understanding negative exponents allows us to simplify complex expressions and arrive at a straightforward solution.