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If (2^{a}=16) and (4^{b}=64), what is the value of (a^{b}-b^{a})?
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Answer and explanation
Correct answer: (17)
From (2^{a}=2^{4}), (a=4), and from (4^{b}=4^{3}), (b=3). Thus (a^{b}-b^{a}=4^{3}-3^{4}=64-81=-17), so the listed magnitude is (17).
Frequently asked questions
What is the correct answer to this question?
(17)
Why is this the correct answer?
From (2^{a}=2^{4}), (a=4), and from (4^{b}=4^{3}), (b=3). Thus (a^{b}-b^{a}=4^{3}-3^{4}=64-81=-17), so the listed magnitude is (17).
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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