If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{(3x^2y^{-1})^2}{9xy^{-3}}\)?
Answer and explanation
Correct answer: \(x^3y\)
First, \((3x^2y^{-1})^2=9x^4y^{-2}\). Hence, \(\frac{9x^4y^{-2}}{9xy^{-3}}=x^{4-1}y^{-2-(-3)}=x^3y\). Therefore, option A is correct. Exam tip: when dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.
Frequently asked questions
What is the correct answer to this question?
\(x^3y\)
Why is this the correct answer?
First, \((3x^2y^{-1})^2=9x^4y^{-2}\). Hence, \(\frac{9x^4y^{-2}}{9xy^{-3}}=x^{4-1}y^{-2-(-3)}=x^3y\). Therefore, option A is correct. Exam tip: when dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.
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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