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If \(x\neq 0\), what is the simplified form of \(\left(2x^{-3}\right)^{-2}\cdot x^{-1}\)?
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Answer and explanation
Correct answer: \(\frac{x^{5}}{4}\)
Here \(\left(2x^{-3}\right)^{-2}=2^{-2}x^{6}=\frac{x^{6}}{4}\), so multiplying by \(x^{-1}\) gives \(\frac{x^{5}}{4}\). In exams, first convert negative exponents carefully.
Frequently asked questions
What is the correct answer to this question?
\(\frac{x^{5}}{4}\)
Why is this the correct answer?
Here \(\left(2x^{-3}\right)^{-2}=2^{-2}x^{6}=\frac{x^{6}}{4}\), so multiplying by \(x^{-1}\) gives \(\frac{x^{5}}{4}\). In exams, first convert negative exponents carefully.
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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