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If \(2^p=5\), what is the value of \(16^p\)?
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Answer and explanation
Correct answer: 625
Rewrite \(16\) as \(2^4\): \(16^p=(2^4)^p=(2^p)^4=5^4=625\). Therefore, the correct answer is 625. The distractor 125 equals \(5^3\), but the required exponent is 4. Exam tip: Express the new base as a power of the given base and apply \((a^m)^n=a^{mn}\).
Frequently asked questions
What is the correct answer to this question?
625
Why is this the correct answer?
Rewrite \(16\) as \(2^4\): \(16^p=(2^4)^p=(2^p)^4=5^4=625\). Therefore, the correct answer is 625. The distractor 125 equals \(5^3\), but the required exponent is 4. Exam tip: Express the new base as a power of the given base and apply \((a^m)^n=a^{mn}\).
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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