If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{x^6y^{-3}}{x^3y^{-5}}\)?
Answer and explanation
Correct answer: \(x^3y^2\)
For division with like bases, subtract the exponent in the denominator from the exponent in the numerator: \(x^{6-3}y^{-3-(-5)}=x^3y^2\). Therefore, \(x^3y^2\) is correct. Option B mishandles the exponents of \(y\), while C and D incorrectly add the exponents of \(x\). Exam tip: when dividing powers with the same base, subtract the denominator exponent from the numerator exponent.
Frequently asked questions
What is the correct answer to this question?
\(x^3y^2\)
Why is this the correct answer?
For division with like bases, subtract the exponent in the denominator from the exponent in the numerator: \(x^{6-3}y^{-3-(-5)}=x^3y^2\). Therefore, \(x^3y^2\) is correct. Option B mishandles the exponents of \(y\), while C and D incorrectly add the exponents of \(x\). Exam tip: when dividing powers with the same base, subtract the denominator exponent from the numerator exponent.
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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