What is the simplified form of \(\frac{3^2\cdot 3^{-4}}{3^{-3}}\)?
Answer and explanation
Correct answer: \(3\)
For powers with the same base, add exponents during multiplication and subtract the denominator's exponent during division: \(2+(-4)-(-3)=1\). Thus, \(3^1=3\), so option A is correct. Option C, \(\frac{1}{3}\), results from incorrectly treating the final exponent as \(-1\). Exam tip: apply \(a^m\div a^n=a^{m-n}\) carefully, especially when the denominator has a negative exponent.
Frequently asked questions
What is the correct answer to this question?
\(3\)
Why is this the correct answer?
For powers with the same base, add exponents during multiplication and subtract the denominator's exponent during division: \(2+(-4)-(-3)=1\). Thus, \(3^1=3\), so option A is correct. Option C, \(\frac{1}{3}\), results from incorrectly treating the final exponent as \(-1\). Exam tip: apply \(a^m\div a^n=a^{m-n}\) carefully, especially when the denominator has a negative exponent.
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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