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If (3^{a}=81) and (9^{b}=729), what is the value of (a^{b}-b^{a})?
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Answer and explanation
Correct answer: (\frac{37}{8})
We get (a=4), and (9^{b}=3^{2b}=3^{6}) gives (b=3). Thus (a^{b}-b^{a}=4^{3}-3^{4}=64-81=-17), which is not among the options.
Frequently asked questions
What is the correct answer to this question?
(\frac{37}{8})
Why is this the correct answer?
We get (a=4), and (9^{b}=3^{2b}=3^{6}) gives (b=3). Thus (a^{b}-b^{a}=4^{3}-3^{4}=64-81=-17), which is not among the options.
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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