What is the value of (\frac{4^3\cdot2^{-1}}{8})?
Answer and explanation
Correct answer: (4)
Rewrite every quantity using base 2. We have \(4^3=(2^2)^3=2^6\u0005, \(2^{-1}\u0005 remains as it is, and \(8=2^3\u0005. Therefore the expression becomes \(\frac{2^6\cdot2^{-1}}{2^3}\u0005. Using exponent laws, multiplication adds exponents and division subtracts them, so the total exponent is \(6+(-1)-3=2\u0005.
Thus the value is \(2^2=4\u0005, making option B correct. The negative exponent means reciprocal, since \(2^{-1}=\frac12\u0005; it does not mean that the final answer is negative. Direct calculation also gives \(64\cdot\frac12\div8=4\u0005.
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
Rewrite every quantity using base 2. We have \(4^3=(2^2)^3=2^6\u0005, \(2^{-1}\u0005 remains as it is, and \(8=2^3\u0005. Therefore the expression becomes \(\frac{2^6\cdot2^{-1}}{2^3}\u0005. Using exponent laws, multiplication adds exponents and division subtracts them, so the total exponent is \(6+(-1)-3=2\u0005.
Thus the value is \(2^2=4\u0005, making option B correct. The negative exponent means reciprocal, since \(2^{-1}=\frac12\u0005; it does not mean that the final answer is negative. Direct calculation also gives \(64\cdot\frac12\div8=4\u0005.
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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