If \(a\) and \(b\) are non-zero real numbers and \(m,n\) are integers, which of the following law of exponents is always valid?
Answer and explanation
Correct answer: \(a^m\cdot a^n=a^{m+n}\)
When powers with the same base are multiplied, their exponents are added, so \(a^m\cdot a^n=a^{m+n}\). In option B, exponents multiply: \((a^m)^n=a^{mn}\). Exam tip: first check whether the bases are the same before applying an exponent law.
Frequently asked questions
What is the correct answer to this question?
\(a^m\cdot a^n=a^{m+n}\)
Why is this the correct answer?
When powers with the same base are multiplied, their exponents are added, so \(a^m\cdot a^n=a^{m+n}\). In option B, exponents multiply: \((a^m)^n=a^{mn}\). Exam tip: first check whether the bases are the same before applying an exponent law.
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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