What is value of ( (2^3 \cdot 4^{-1}) )
Answer and explanation
Correct answer: 2
Since 4 = 2^2, we have \(4^{-1} = (2^2)^{-1} = 2^{-2}\). Therefore, \(2^3 \cdot 4^{-1} = 2^3 \cdot 2^{-2} = 2^{3-2} = 2\). Hence, option A is correct. Exam tip: When multiplying powers with the same base, subtract the exponents; you can also verify a negative exponent by taking the reciprocal.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Since 4 = 2^2, we have \(4^{-1} = (2^2)^{-1} = 2^{-2}\). Therefore, \(2^3 \cdot 4^{-1} = 2^3 \cdot 2^{-2} = 2^{3-2} = 2\). Hence, option A is correct. Exam tip: When multiplying powers with the same base, subtract the exponents; you can also verify a negative exponent by taking the reciprocal.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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