If a and b are positive integers and (2^a)^b=2^3, what is the value of 2^a 2^b ?

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16 We rewrite the left side using exponent rules and then set the exponents equal because the base is 2 on both sides. (2^a)^b = 2^3 2^a b = 2^3 a b = 3 We list the positive integer pairs that multiply to 3. a b = 3 (a,b) = (1,3) or (3,1) We add the exponents to get 4 and then evaluate the corresponding power of two. 2^a 2^b = 2^a + b = 2^4 = 16

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$We rewrite the left side using exponent rules and then set the exponents equal because the base is 2 on both sides.$	$(2^{a})^{b} = 2^{3} 2^{ab} = 2^{3} ab = 3$
$We list the positive integer pairs that multiply to 3.$	$a \times b = 3 (a, b) = (1, 3) or (3, 1)$
$We add the exponents to get 4 and then evaluate the corresponding power of two.$	$2^{a} \times 2^{b} = 2^{a + b} = 2^{4} = 16$

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