If $a$ and $b$ are positive integers and $\left(2^{a}\right)^{b}=2^{3}$, what is the value of $2^{a} 2^{b}$ ?

If $a$ and $b$ are positive integers and $\left(2^... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

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

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and then set the exponents equal because the base is 2 on both sides.$	$(2^{a})^{b} = 2^{3} 2^{ab} = 2^{3} ab = 3$	Theory & Tactics Method Card ALG7 Click to view full details
$We list the positive integer pairs that multiply to 3.$	$a \times b = 3 (a, b) = (1, 3) or (3, 1)$
$We add the exponents to get 4 and then evaluate the corresponding power of two.$	$2^{a} \times 2^{b} = 2^{a + b} = 2^{4} = 16$

Scroll horizontally to view all columns

16

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

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and then set the exponents equal because the base is 2 on both sides.$	$(2^{a})^{b} = 2^{3} 2^{ab} = 2^{3} ab = 3$	Theory & Tactics Method Card ALG7 Click to view full details
$We list the positive integer pairs that multiply to 3.$	$a \times b = 3 (a, b) = (1, 3) or (3, 1)$
$We add the exponents to get 4 and then evaluate the corresponding power of two.$	$2^{a} \times 2^{b} = 2^{a + b} = 2^{4} = 16$

Scroll horizontally to view all columns

16