What is the value of \(((5^2)^2\div 5^3)\)?
Answer and explanation
Correct answer: 5
Use the exponent rules \((a^m)^n=a^{mn}\) and \(a^m\div a^n=a^{m-n}\). Thus, \((5^2)^2\div 5^3=5^{2\times 2}\div 5^3=5^4\div 5^3=5^{4-3}=5\). Therefore, option B is correct. Option C, \(25=5^2\), can result from stopping after the power-of-a-power step or subtracting the exponents incorrectly. Exam tip: when dividing powers with the same base, subtract the exponents.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Use the exponent rules \((a^m)^n=a^{mn}\) and \(a^m\div a^n=a^{m-n}\). Thus, \((5^2)^2\div 5^3=5^{2\times 2}\div 5^3=5^4\div 5^3=5^{4-3}=5\). Therefore, option B is correct. Option C, \(25=5^2\), can result from stopping after the power-of-a-power step or subtracting the exponents incorrectly. Exam tip: when dividing powers with the same base, subtract the exponents.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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