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Find (81^{1/2}\times81^{1/2}).
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Answer and explanation
Correct answer: 81
When powers with the same base are multiplied, their exponents are added: \(81^{1/2}\times81^{1/2}=81^{(1/2+1/2)}=81^1=81\). The value 9 represents only one factor, \(81^{1/2}\), not the complete product. Exam tip: use the rule \(a^m\times a^n=a^{m+n}\) for equal bases.
Frequently asked questions
What is the correct answer to this question?
81
Why is this the correct answer?
When powers with the same base are multiplied, their exponents are added: \(81^{1/2}\times81^{1/2}=81^{(1/2+1/2)}=81^1=81\). The value 9 represents only one factor, \(81^{1/2}\), not the complete product. Exam tip: use the rule \(a^m\times a^n=a^{m+n}\) for equal bases.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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