(3/5)^-1

2 min read Jun 16, 2024
(3/5)^-1

Understanding (3/5)^-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 (3/5)^-1 means and how to calculate it:

The Basics of Negative Exponents

  • Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2 is 1/2.
  • Negative Exponent Rule: x^-n = 1/x^n

Calculating (3/5)^-1

Applying the negative exponent rule, we can rewrite (3/5)^-1 as:

(3/5)^-1 = 1/(3/5)^1

Since any number raised to the power of 1 is itself, we have:

1/(3/5)^1 = 1/(3/5)

To divide by a fraction, we multiply by its reciprocal:

1/(3/5) = 1 * (5/3) = 5/3

Conclusion

Therefore, (3/5)^-1 is equivalent to 5/3.

This demonstrates that understanding negative exponents allows us to simplify seemingly complex expressions and arrive at a clear and concise result.

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