What is the value of ((2^3\times2^2)^2)?
Answer and explanation
Correct answer: 1024
For powers with the same base, the exponents are added: \(2^3\times2^2=2^{3+2}=2^5\). Then \((2^5)^2=2^{5\times2}=2^{10}=1024\). Therefore, option B is correct. Option C, 512, equals \(2^9\) and may result from applying the outer exponent incorrectly. Exam tip: remember \(a^m\times a^n=a^{m+n}\) and \((a^m)^n=a^{mn}\).
Frequently asked questions
What is the correct answer to this question?
1024
Why is this the correct answer?
For powers with the same base, the exponents are added: \(2^3\times2^2=2^{3+2}=2^5\). Then \((2^5)^2=2^{5\times2}=2^{10}=1024\). Therefore, option B is correct. Option C, 512, equals \(2^9\) and may result from applying the outer exponent incorrectly. Exam tip: remember \(a^m\times a^n=a^{m+n}\) and \((a^m)^n=a^{mn}\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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