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If \(x\neq0\), what is the simplified form of \(\left(\frac{2x^{-3}}{x^{2}}\right)^{-2}\cdot x^{-4}\)?
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Answer and explanation
Correct answer: \(\frac{x^{6}}{4}\)
Inside, \(\frac{2x^{-3}}{x^{2}}=2x^{-5}\), so \(\left(2x^{-5}\right)^{-2}x^{-4}=\frac{x^{10}}{4}x^{-4}=\frac{x^{6}}{4}\). In exams, subtract the inner exponents first.
Frequently asked questions
What is the correct answer to this question?
\(\frac{x^{6}}{4}\)
Why is this the correct answer?
Inside, \(\frac{2x^{-3}}{x^{2}}=2x^{-5}\), so \(\left(2x^{-5}\right)^{-2}x^{-4}=\frac{x^{10}}{4}x^{-4}=\frac{x^{6}}{4}\). In exams, subtract the inner exponents 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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