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(4/7)^-1

2 min read Jun 16, 2024
(4/7)^-1

Understanding (4/7)^-1

In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. Let's break down (4/7)^-1:

The Basics

  • Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2 is 1/2.
  • Negative Exponent: A negative exponent signifies taking the reciprocal of the base raised to the positive version of the exponent.

Solving (4/7)^-1

  1. Find the reciprocal of the base: The base is (4/7). Its reciprocal is (7/4).
  2. Raise the reciprocal to the positive exponent: The exponent is -1. The positive version is 1. So, we raise (7/4) to the power of 1.
  3. Simplify: (7/4)^1 is simply (7/4).

The Answer

Therefore, (4/7)^-1 is equal to 7/4.

Key takeaway: Remember that a negative exponent always means taking the reciprocal of the base raised to the positive version of the exponent.

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