%5E-1.jpeg "(6/7)^-1")
Understanding (6/7)^-1
In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. Let's break down (6/7)^-1.
Reciprocals
The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 5 is 1/5.
Negative Exponents
When dealing with negative exponents, we follow the rule:
x^-n = 1/x^n
This means (6/7)^-1 is the same as 1/(6/7)^1.
Simplifying (6/7)^-1
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Calculate (6/7)^1: Any number raised to the power of 1 is itself, so (6/7)^1 = 6/7.
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Find the reciprocal: The reciprocal of 6/7 is 7/6.
Therefore, (6/7)^-1 = 7/6.
Key Takeaways
- Negative exponents indicate reciprocals.
- (x/y)^-n = (y/x)^n
By understanding these concepts, you can easily work with negative exponents in fractions.