What is the value of \(\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{2}\right)^{-2}\)?
Answer and explanation
Correct answer: \(13\)
Using the negative-exponent rule \(a^{-n}=\frac{1}{a^n}\), we get \(\left(\frac{1}{3}\right)^{-2}=3^2=9\) and \(\left(\frac{1}{2}\right)^{-2}=2^2=4\). Therefore, the sum is \(9+4=13\). The value \(\frac{13}{36}\) results from mishandling the negative powers of the fractions. Exam tip: for a negative exponent, take the reciprocal of the base before applying the exponent.
Frequently asked questions
What is the correct answer to this question?
\(13\)
Why is this the correct answer?
Using the negative-exponent rule \(a^{-n}=\frac{1}{a^n}\), we get \(\left(\frac{1}{3}\right)^{-2}=3^2=9\) and \(\left(\frac{1}{2}\right)^{-2}=2^2=4\). Therefore, the sum is \(9+4=13\). The value \(\frac{13}{36}\) results from mishandling the negative powers of the fractions. Exam tip: for a negative exponent, take the reciprocal of the base before applying the exponent.
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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