What is simplified form of \((x^3 y^{-3})^{-1}\)
Answer and explanation
Correct answer: \(\frac{y^3}{x^3}\)
First, \(y^{-3}=\frac{1}{y^3}\), so \(x^3y^{-3}=\frac{x^3}{y^3}\). The exponent \(-1\) on the entire expression takes the reciprocal: \(\left(\frac{x^3}{y^3}\right)^{-1}=\frac{y^3}{x^3}\). Therefore, option A is correct. Here, \(x\) and \(y\) are assumed to be nonzero. Exam tip: remember \(a^{-n}=\frac{1}{a^n}\) and \(\left(\frac{a}{b}\right)^{-1}=\frac{b}{a}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{y^3}{x^3}\)
Why is this the correct answer?
First, \(y^{-3}=\frac{1}{y^3}\), so \(x^3y^{-3}=\frac{x^3}{y^3}\). The exponent \(-1\) on the entire expression takes the reciprocal: \(\left(\frac{x^3}{y^3}\right)^{-1}=\frac{y^3}{x^3}\). Therefore, option A is correct. Here, \(x\) and \(y\) are assumed to be nonzero. Exam tip: remember \(a^{-n}=\frac{1}{a^n}\) and \(\left(\frac{a}{b}\right)^{-1}=\frac{b}{a}\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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