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What is the value of ((3^2)^3\div3^4)?
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Answer and explanation
Correct answer: 9
Using the power-of-a-power rule, \((3^2)^3=3^{2\times3}=3^6\). For division with the same base, subtract the exponents: \(3^6\div3^4=3^{6-4}=3^2=9\). Therefore, the correct answer is 9. Exam tip: simplify the nested power first, then subtract exponents when dividing like bases.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Using the power-of-a-power rule, \((3^2)^3=3^{2\times3}=3^6\). For division with the same base, subtract the exponents: \(3^6\div3^4=3^{6-4}=3^2=9\). Therefore, the correct answer is 9. Exam tip: simplify the nested power first, then subtract exponents when dividing like 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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