If \(a=2\), what is the value of \(a^3+a^{-1}\)?
Answer and explanation
Correct answer: \(\frac{17}{2}\)
Given \(a=2\), we have \(a^3=2^3=8\). By the negative exponent rule, \(a^{-1}=\frac{1}{a}=\frac{1}{2}\). Therefore, \(a^3+a^{-1}=8+\frac{1}{2}=\frac{17}{2}\). The value \(\frac{15}{2}\) results from evaluating one of the powers incorrectly. Exam tip: remember that \(x^{-n}=\frac{1}{x^n}\) for \(x\neq0\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{17}{2}\)
Why is this the correct answer?
Given \(a=2\), we have \(a^3=2^3=8\). By the negative exponent rule, \(a^{-1}=\frac{1}{a}=\frac{1}{2}\). Therefore, \(a^3+a^{-1}=8+\frac{1}{2}=\frac{17}{2}\). The value \(\frac{15}{2}\) results from evaluating one of the powers incorrectly. Exam tip: remember that \(x^{-n}=\frac{1}{x^n}\) for \(x\neq0\).
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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