Question
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Answer
\(-5^{-2} = -\frac{1}{25}\)
Solution
To evaluate the expression \( -5^{-2} \), it's important to follow the order of operations (also known as PEMDAS/BODMAS):
1. **Exponents**: Handle the exponentiation first.
2. **Negation**: Apply the negative sign after exponentiation.
Let's break it down step by step:
1. **Calculate the Exponent:**
\( 5^{-2} \) means \( \frac{1}{5^2} \).
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
2. **Apply the Negative Sign:**
The expression has a negative sign in front of \( 5^{-2} \), so:
\[
-5^{-2} = -\left( \frac{1}{25} \right) = -\frac{1}{25}
\]
**Final Answer:**
\[
-5^{-2} = -\frac{1}{25}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Did you know that when you raise a negative number to an even power, the result is always positive? So, when you calculate \( -5^{-2} \), it’s important to remember the negative sign is outside the exponentiation. First, you take \( 5^{-2} \), which equals \( \frac{1}{25} \), and then apply the negative sign, resulting in \( -\frac{1}{25} \). Now, if you ever find yourself confused about signs while dealing with exponents, a great tip is to break it down step by step. Always deal with the exponent first, then apply any negative signs after. This way, you'll avoid common mistakes like accidentally making everything negative before evaluating the exponent!
