What is value of (4^{-1} + 2^{-1})
Answer and explanation
Correct answer: \(\frac{3}{4}\)
Use the negative-exponent rule \(a^{-n}=\frac{1}{a^n}\). Thus, \(4^{-1}=\frac{1}{4}\) and \(2^{-1}=\frac{1}{2}\). Taking a common denominator gives \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\), so option A is correct. \(\frac{1}{8}\) would result from multiplying the two fractions, not adding them. Exam tip: convert negative exponents to reciprocals before performing the operation.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3}{4}\)
Why is this the correct answer?
Use the negative-exponent rule \(a^{-n}=\frac{1}{a^n}\). Thus, \(4^{-1}=\frac{1}{4}\) and \(2^{-1}=\frac{1}{2}\). Taking a common denominator gives \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\), so option A is correct. \(\frac{1}{8}\) would result from multiplying the two fractions, not adding them. Exam tip: convert negative exponents to reciprocals before performing the operation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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