(-7)^-1 Without Exponent

Jasonbradley

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Jun 16, 2024

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Understanding (-7)^-1 Without Exponents

The expression (-7)^-1 might seem intimidating at first glance, especially if you're not familiar with negative exponents. But it's actually quite simple to understand once you break it down.

The Rule of Negative Exponents

The key to understanding negative exponents is this rule: x^-n = 1/x^n.

In simpler terms, a negative exponent means we're taking the reciprocal of the base raised to the positive version of that exponent.

Applying the Rule

Let's apply this rule to our expression (-7)^-1:

1. Identify the base and exponent:

   • Base: -7
   • Exponent: -1

2. Apply the rule:

   • (-7)^-1 = 1/(-7)^1

3. Simplify:

   • 1/(-7)^1 = 1/-7 = -1/7

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

Conclusion

While negative exponents might look complicated, the rule is straightforward. By applying this rule, we can easily express any number with a negative exponent as a fraction. In this case, we found that (-7)^-1 simplifies to -1/7.