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Subjects
Class 10MathematicsPolynomialsOperations on real numbers and the laws of exponentsExpertLevel 45
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If \(x\neq0\), what is the simplified form of \(\left(\frac{4x^{-2}}{x^{3}}\right)^{-1}\cdot x^{-4}\)?

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Answer and explanation

Correct answer: \(\frac{x}{4}\)

Here \(\frac{4x^{-2}}{x^{3}}=4x^{-5}\), so its reciprocal is \(\frac{x^{5}}{4}\), and multiplying by \(x^{-4}\) gives \(\frac{x}{4}\). In exams, simplify the bracket first.

Related tags

ExponentsNegative ExponentsPolynomials

Frequently asked questions

What is the correct answer to this question?

\(\frac{x}{4}\)

Why is this the correct answer?

Here \(\frac{4x^{-2}}{x^{3}}=4x^{-5}\), so its reciprocal is \(\frac{x^{5}}{4}\), and multiplying by \(x^{-4}\) gives \(\frac{x}{4}\). In exams, simplify the bracket first.

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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  1. 1Which option gives the correct value of 1/(√10 − 3)?
  2. 2What is the value of (2^3\cdot2^4)?
  3. 3What is the simplified form of (\frac{5^6}{5^2})?
  4. 4What is the simplified form of ((3^2)^4)?
  5. 5If \(a\ne0\), what is the value of \(a^0\)?
  6. 6What is (10^{-2}) equal to?
  7. 7What is the simplified form of ((2\cdot5)^3)?
  8. 8What is the value of \(\left(\frac{3}{4}\right)^2\)?
  9. 9Which of the following expressions is equal to \(7^2\cdot 7^3\)?
  10. 10What is the simplified form of (9^5\div9^3)?
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