If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\frac{x^8y^{-4}}{x^5y^{-6}}\)?
Answer and explanation
Correct answer: \(x^3y^2\)
When dividing powers with the same base, subtract the exponents: \(x^{8-5}y^{-4-(-6)}=x^3y^2\). Therefore, option A is correct. In option B, the exponent of \(y\) is calculated incorrectly, while options C and D add the exponents instead of subtracting them. Exam tip: use \(a^m\div a^n=a^{m-n}\) when dividing like bases.
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: \(x^{8-5}y^{-4-(-6)}=x^3y^2\). Therefore, option A is correct. In option B, the exponent of \(y\) is calculated incorrectly, while options C and D add the exponents instead of subtracting them. Exam tip: use \(a^m\div a^n=a^{m-n}\) when dividing like bases.
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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