Using the laws of exponents for like bases, what is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?
Answer and explanation
Correct answer: \(2^2\)
When powers with the same base are multiplied, their exponents are added: \(2^3\cdot2^{-5}\cdot2^4=2^{3+(-5)+4}=2^2\). Therefore, option A is correct. Option B results from mishandling the negative exponent, while option D incorrectly multiplies the exponents. In an exam, retain the sign of a negative exponent while adding exponents.
Frequently asked questions
What is the correct answer to this question?
\(2^2\)
Why is this the correct answer?
When powers with the same base are multiplied, their exponents are added: \(2^3\cdot2^{-5}\cdot2^4=2^{3+(-5)+4}=2^2\). Therefore, option A is correct. Option B results from mishandling the negative exponent, while option D incorrectly multiplies the exponents. In an exam, retain the sign of a negative exponent while adding exponents.
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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