GMAT prep

[superrrom]

Thanks

[cramya]

We need to get the bases to match on LHS and RHS

5 ^ 21 * 4 * 11 = 2 * 10 ^ N

<=> 5 ^ 21 * 2 ^ 22 = 2 * 10 ^ N (4 = 2 ^ 2 using formula (a^b)^c = a ^ (b*c) where a= 2 b =2 c = 11)
<=> 5 ^ 21 * 2 ^ 21 * 2 = 2 * 10 ^ N (splitting 2 ^ 22 as 2 ^ 21 * (2 ^ 1 which is 2)
<=> 2 * (10) ^ 21 = 2 * 10 ^ N (5 ^ 21 and 2 ^ 21 can be combined as 10 ^ 21 using the exponent rule (a^n * b ^n = (ab)^n)

N = 21

[Azntycoon]

(5^21)(4^11) = (2)(10^n)
(5^21)(2^2)^11) = (2)(10^n)
(5^21)(2^22) = (2)(10^n)
(5^21)(2^21)(2) = (2)(10^n)
(2)(10^21) = (2)(10^n)

Eliminate the bases (2 and 10), leaving you with n = 21

ps. I think this question has been posted before, so pls 2x check as per rules of this board.