If \(a>0\) and \(p,q\) are real numbers, which of the following laws of exponents is always correct?
Answer and explanation
Correct answer: \(a^p\cdot a^q=a^{p+q}\)
When powers with the same positive base are multiplied, their exponents are added; hence \(a^p\cdot a^q=a^{p+q}\). In division, exponents are subtracted, not divided: \(a^p/a^q=a^{p-q}\). Exam tip: multiply → add exponents; divide → subtract.
Frequently asked questions
What is the correct answer to this question?
\(a^p\cdot a^q=a^{p+q}\)
Why is this the correct answer?
When powers with the same positive base are multiplied, their exponents are added; hence \(a^p\cdot a^q=a^{p+q}\). In division, exponents are subtracted, not divided: \(a^p/a^q=a^{p-q}\). Exam tip: multiply → add exponents; divide → subtract.
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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