If \(m\neq 0\) and \(n\neq 0\), what is the simplified form of \(\left(\frac{m^{-4}n^{3}}{m^{2}n^{-5}}\right)^{-1}\)?
Answer and explanation
Correct answer: \(m^{6}n^{-8}\)
Using the quotient rule for exponents, \(\frac{m^{-4}n^3}{m^2n^{-5}}=m^{-4-2}n^{3-(-5)}=m^{-6}n^8\). Raising this result to the power \(-1\) takes its reciprocal: \((m^{-6}n^8)^{-1}=m^6n^{-8}\). Therefore, option B is correct. Exam tip: a negative exponent represents a reciprocal, so \(n^{-8}=\frac{1}{n^8}\).
Frequently asked questions
What is the correct answer to this question?
\(m^{6}n^{-8}\)
Why is this the correct answer?
Using the quotient rule for exponents, \(\frac{m^{-4}n^3}{m^2n^{-5}}=m^{-4-2}n^{3-(-5)}=m^{-6}n^8\). Raising this result to the power \(-1\) takes its reciprocal: \((m^{-6}n^8)^{-1}=m^6n^{-8}\). Therefore, option B is correct. Exam tip: a negative exponent represents a reciprocal, so \(n^{-8}=\frac{1}{n^8}\).
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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