What is the value of \((2^{11}\div(2^2)^4)\)?
Answer and explanation
Correct answer: 8
First, using the power-of-a-power rule, \((2^2)^4=2^{2\times4}=2^8\). Therefore, \(2^{11}\div2^8=2^{11-8}=2^3=8\), so option A is correct. Option B results from incorrectly applying the exponent rule during division. Exam tip: multiply exponents in a power of a power and subtract exponents when dividing like bases.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
First, using the power-of-a-power rule, \((2^2)^4=2^{2\times4}=2^8\). Therefore, \(2^{11}\div2^8=2^{11-8}=2^3=8\), so option A is correct. Option B results from incorrectly applying the exponent rule during division. Exam tip: multiply exponents in a power of a power and subtract exponents when dividing like bases.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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