Question
If a base is negative, how will you know whether the answer is positive or negative before evaluating it?
Answers
Answered by
GPT-4o mini
When dealing with expressions that involve a negative base raised to a power, the sign of the result can be determined based on the exponent used. Here are the key rules:
1. **Odd Exponent**: If the exponent is an odd number, raising a negative base to that power will result in a negative value. For example, \((-2)^3 = -8\).
2. **Even Exponent**: If the exponent is an even number, raising a negative base to that power will result in a positive value. For example, \((-2)^2 = 4\).
3. **Zero Exponent**: Any non-zero number (including a negative base) raised to the exponent of 0 is 1. For example, \((-2)^0 = 1\).
In summary, to predict the sign of the result when a negative base is raised to a power, you only need to look at the exponent:
- Odd exponent = negative result
- Even exponent = positive result
- Zero exponent = positive result (specifically 1)
1. **Odd Exponent**: If the exponent is an odd number, raising a negative base to that power will result in a negative value. For example, \((-2)^3 = -8\).
2. **Even Exponent**: If the exponent is an even number, raising a negative base to that power will result in a positive value. For example, \((-2)^2 = 4\).
3. **Zero Exponent**: Any non-zero number (including a negative base) raised to the exponent of 0 is 1. For example, \((-2)^0 = 1\).
In summary, to predict the sign of the result when a negative base is raised to a power, you only need to look at the exponent:
- Odd exponent = negative result
- Even exponent = positive result
- Zero exponent = positive result (specifically 1)
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