What is the simplified form of \(\frac{x^5y^{-2}}{x^2y^{-4}}\), if \(x\neq0\) and \(y\neq0\)?
Answer and explanation
Correct answer: \(x^3y^2\)
When dividing powers with the same base, subtract the exponents: \(x^{5-2}=x^3\) and \(y^{-2-(-4)}=y^2\). Therefore, the simplified form is \(x^3y^2\). Option B results from adding the exponents, but division requires their subtraction. Exam tip: Use parentheses carefully when subtracting a negative exponent, as in \(-2-(-4)=2\).
Frequently asked questions
What is the correct answer to this question?
\(x^3y^2\)
Why is this the correct answer?
When dividing powers with the same base, subtract the exponents: \(x^{5-2}=x^3\) and \(y^{-2-(-4)}=y^2\). Therefore, the simplified form is \(x^3y^2\). Option B results from adding the exponents, but division requires their subtraction. Exam tip: Use parentheses carefully when subtracting a negative exponent, as in \(-2-(-4)=2\).
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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