If \(x\neq0\) and \(y\neq0\), what is the simplified form of \(\left(\frac{x^{-2}}{y^{-3}}\right)^{-1}\)?
Answer and explanation
Correct answer: \(\frac{x^2}{y^3}\)
First, \(\frac{x^{-2}}{y^{-3}}=x^{-2}\times y^3=\frac{y^3}{x^2}\). Raising this expression to the power \(-1\) gives its reciprocal: \(\left(\frac{y^3}{x^2}\right)^{-1}=\frac{x^2}{y^3}\). Option C is only the form inside the outer power, not the final answer. Exam tip: \(a^{-1}\) means \(\frac{1}{a}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{x^2}{y^3}\)
Why is this the correct answer?
First, \(\frac{x^{-2}}{y^{-3}}=x^{-2}\times y^3=\frac{y^3}{x^2}\). Raising this expression to the power \(-1\) gives its reciprocal: \(\left(\frac{y^3}{x^2}\right)^{-1}=\frac{x^2}{y^3}\). Option C is only the form inside the outer power, not the final answer. Exam tip: \(a^{-1}\) means \(\frac{1}{a}\).
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
