What is the value of \(4^{-1}+2^{-2}\)?
Answer and explanation
Correct answer: \(\frac{1}{2}\)
Use the law of negative exponents: \(a^{-n}=\frac{1}{a^n}\). Thus, \(4^{-1}=\frac{1}{4}\) and \(2^{-2}=\frac{1}{2^2}=\frac{1}{4}\). Therefore, \(\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\), so option A is correct. Exam tip: Convert negative powers into reciprocals before performing the addition.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{2}\)
Why is this the correct answer?
Use the law of negative exponents: \(a^{-n}=\frac{1}{a^n}\). Thus, \(4^{-1}=\frac{1}{4}\) and \(2^{-2}=\frac{1}{2^2}=\frac{1}{4}\). Therefore, \(\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\), so option A is correct. Exam tip: Convert negative powers into reciprocals before performing the addition.
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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