(6/7)^-1

2 min read Jun 16, 2024
(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

  1. Calculate (6/7)^1: Any number raised to the power of 1 is itself, so (6/7)^1 = 6/7.

  2. 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.

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