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What is the value of \(3^5\cdot 9^{-1}\)?
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Answer and explanation
Correct answer: 27
Since \(9=3^2\), we have \(9^{-1}=(3^2)^{-1}=3^{-2}\). Therefore, \(3^5\cdot 9^{-1}=3^5\cdot 3^{-2}=3^{5-2}=3^3=27\), so option B is correct. Exam tip: When multiplying powers with the same base, add their exponents.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Since \(9=3^2\), we have \(9^{-1}=(3^2)^{-1}=3^{-2}\). Therefore, \(3^5\cdot 9^{-1}=3^5\cdot 3^{-2}=3^{5-2}=3^3=27\), so option B is correct. Exam tip: When multiplying powers with the same base, add their exponents.
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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