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If a and b are positive integers and $2^{(a)b} = 2^{3}$, what is the value of $2^{a}2^{b}$?
in A Level Maths by Diamond (47.6k points) | 30 views

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(2^(a)b)) = (2^3) = (2^(ab))

This implies that ab = 3

But 3 has only two factors, which are 3 and 1.

This implies 3 = 3 x 1 = 1 x 3

When a = 1; b = 3. When a = 3; b = 1.

(2^a)(2^b) = (2^(a+b)) = 2^(1+3) or 2^(3+1) = 2^4 = 16.
by Gold Status (22.7k points)

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