If \(x\) and \(y\) are non-zero real numbers and \(\left(x^{-3}y^{2}\right)^k=x^{-12}y^{8}\), what is the value of \(k\)?
Answer and explanation
Correct answer: 4
Using the exponent rule \((ab)^k=a^k b^k\), the left-hand side becomes \(x^{-3k}y^{2k}\). Comparing the exponents of the same bases gives \(-3k=-12\) and \(2k=8\), and both equations yield \(k=4\). Exam tip: When monomials with the same bases are equal, compare the corresponding exponents.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Using the exponent rule \((ab)^k=a^k b^k\), the left-hand side becomes \(x^{-3k}y^{2k}\). Comparing the exponents of the same bases gives \(-3k=-12\) and \(2k=8\), and both equations yield \(k=4\). Exam tip: When monomials with the same bases are equal, compare the corresponding exponents.
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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