If $r$ and $s$ are positive integers and $(3^{r})^... | 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 r and s are positive integers and (3^{r})^{s} = 3^{5}, what is the value of 3^{r} \times 3^{s} ?

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and match exponents since the base is 3 on both sides, then apply Prime Matching .$	$(3^{r})^{s} = 3^{5} 3^{rs} = 3^{5} rs = 5$	Theory & Tactics Method Card ALG7 Click to view full details
$We list the positive integer pairs that multiply to 5.$	$r \times s = 5 (r, s) = (1, 5) or (5, 1)$
$We add the exponents to write the product as a single power of 3 and then evaluate it.$	$3^{r} \times 3^{s} = 3^{r + s} = 3^{6} = 729$

Scroll horizontally to view all columns

C

If r and s are positive integers and (3^{r})^{s} = 3^{5}, what is the value of 3^{r} \times 3^{s} ?

Explanation	Calculations	Help
$We rewrite the left side using exponent rules and match exponents since the base is 3 on both sides, then apply Prime Matching .$	$(3^{r})^{s} = 3^{5} 3^{rs} = 3^{5} rs = 5$	Theory & Tactics Method Card ALG7 Click to view full details
$We list the positive integer pairs that multiply to 5.$	$r \times s = 5 (r, s) = (1, 5) or (5, 1)$
$We add the exponents to write the product as a single power of 3 and then evaluate it.$	$3^{r} \times 3^{s} = 3^{r + s} = 3^{6} = 729$

Scroll horizontally to view all columns

C