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For real exponents \(m\) and \(n\), which condition on the base \(a\) is appropriate for using the exponent law \(a^m \times a^n=a^{m+n}\) in general?
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Answer and explanation
Correct answer: \(a>0\)
For real exponents, \(a^m\) is generally defined for \(a>0\), so the product law applies safely. With \(a<0\), some irrational powers are not real. Exam tip: whenever real exponents appear, first check that the base is positive.
Frequently asked questions
What is the correct answer to this question?
\(a>0\)
Why is this the correct answer?
For real exponents, \(a^m\) is generally defined for \(a>0\), so the product law applies safely. With \(a<0\), some irrational powers are not real. Exam tip: whenever real exponents appear, first check that the base is positive.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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