What is the value of ((2^5)^2\div2^8)?
Answer and explanation
Correct answer: 4
Using the power-of-a-power rule, \((a^m)^n=a^{mn}\), we get \((2^5)^2=2^{10}\). For division with the same base, subtract the exponents: \(2^{10}\div2^8=2^{10-8}=2^2=4\). Therefore, the correct answer is 4. Exam tip: multiply exponents in a power raised to another power, then subtract exponents when dividing like bases.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Using the power-of-a-power rule, \((a^m)^n=a^{mn}\), we get \((2^5)^2=2^{10}\). For division with the same base, subtract the exponents: \(2^{10}\div2^8=2^{10-8}=2^2=4\). Therefore, the correct answer is 4. Exam tip: multiply exponents in a power raised to another power, then 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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