What is simplified form of ((a^2 b^{-2}))
Answer and explanation
Correct answer: \(\frac{a^2}{b^2}\)
Using the negative-exponent rule, \(b^{-2}=\frac{1}{b^2}\), for \(b\neq0\). Hence, \(a^2b^{-2}=a^2\times\frac{1}{b^2}=\frac{a^2}{b^2}\). Option B reverses the numerator and denominator, while option C incorrectly changes the negative exponent to a positive one without taking the reciprocal. Exam tip: move a factor with a negative exponent across the fraction bar and change the exponent to positive.
Frequently asked questions
What is the correct answer to this question?
\(\frac{a^2}{b^2}\)
Why is this the correct answer?
Using the negative-exponent rule, \(b^{-2}=\frac{1}{b^2}\), for \(b\neq0\). Hence, \(a^2b^{-2}=a^2\times\frac{1}{b^2}=\frac{a^2}{b^2}\). Option B reverses the numerator and denominator, while option C incorrectly changes the negative exponent to a positive one without taking the reciprocal. Exam tip: move a factor with a negative exponent across the fraction bar and change the exponent to positive.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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