What is the simplified form of the product of powers with the same base, \(2^3\cdot2^0\cdot2^2\)?
Answer and explanation
Correct answer: \(2^5\)
When powers with the same base are multiplied, their exponents are added: \(2^3\cdot2^0\cdot2^2=2^{3+0+2}=2^5\). Therefore, \(2^5\) is correct. The distractor \(2^6\) results from incorrectly treating the exponent 0 as 1. Exam tip: for every non-zero number, \(a^0=1\).
Frequently asked questions
What is the correct answer to this question?
\(2^5\)
Why is this the correct answer?
When powers with the same base are multiplied, their exponents are added: \(2^3\cdot2^0\cdot2^2=2^{3+0+2}=2^5\). Therefore, \(2^5\) is correct. The distractor \(2^6\) results from incorrectly treating the exponent 0 as 1. Exam tip: for every non-zero number, \(a^0=1\).
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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