If \(a=5\), what is the value of \(a^2-a^{-1}\)?
Answer and explanation
Correct answer: \(\frac{124}{5}\)
By the law of exponents, \(a^{-1}=\frac{1}{a}\). Therefore, \(5^2-5^{-1}=25-\frac{1}{5}=\frac{125-1}{5}=\frac{124}{5}\). Option B results from incorrectly adding 1 in the numerator instead of subtracting it. In an exam, remember that a negative exponent represents the reciprocal of the base.
Frequently asked questions
What is the correct answer to this question?
\(\frac{124}{5}\)
Why is this the correct answer?
By the law of exponents, \(a^{-1}=\frac{1}{a}\). Therefore, \(5^2-5^{-1}=25-\frac{1}{5}=\frac{125-1}{5}=\frac{124}{5}\). Option B results from incorrectly adding 1 in the numerator instead of subtracting it. In an exam, remember that a negative exponent represents the reciprocal of the base.
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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