What is the value of \(9^{-1}+3^{-2}\)?
Answer and explanation
Correct answer: \(\frac{2}{9}\)
Using the negative exponent rule \(a^{-n}=\frac{1}{a^n}\), we get \(9^{-1}=\frac{1}{9}\) and \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). Therefore, the sum is \(\frac{1}{9}+\frac{1}{9}=\frac{2}{9}\). A useful exam tip is to convert negative powers into reciprocals before performing the operation.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2}{9}\)
Why is this the correct answer?
Using the negative exponent rule \(a^{-n}=\frac{1}{a^n}\), we get \(9^{-1}=\frac{1}{9}\) and \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). Therefore, the sum is \(\frac{1}{9}+\frac{1}{9}=\frac{2}{9}\). A useful exam tip is to convert negative powers into reciprocals before performing the operation.
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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