GMAT Prep ques.

MarkIppo · Posted: Tue Apr 03, 2007 12:40 pm Post subject: GMAT Prep ques.

This one is probably easy for you guys, but it is stumping me.

5^21 x 4^11=2 x 10^n

Reads: 5 to the 21st power mult. by 4 to the 11th power equals 2 mult by 10 to the nth power. What is n?

I know the answer because I took the practice test, but how does one get there?

gmatme · Posted: Tue Apr 03, 2007 1:42 pm Post subject:

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

So n = 21.

vk.neni · Posted: Tue Apr 03, 2007 1:43 pm Post subject:

Reorganizing the following equation a little differently leads us to the answer quite quickly.

5^21 x 4^11=2 x 10^n

5^21 x (2^2)^11 = 2 x 10^n

5^21 x 2^22 = 2 x 10^n

(5x2)^21 x 2 = 2 x 10^n

10^21 = 10^n

So n=21.

-Neni

Cybermusings · Posted: Wed Apr 04, 2007 3:57 am Post subject:

5^21 x 4^11=2 x 10^n

5^21 x (2^2)^11= 2 x 10^n

5^21 x 2^22 = 2 x 10^n

5^21 x 2^21 x 2 = 2 x 10^n

10^21 x 2 = 2 x 10^n

10^21 = 10^n

Thus n = 21

vinviper1 · Posted: Mon May 12, 2008 10:34 am Post subject:

(2^2)^11 = 2^22

Is this a rule of some sort that can be used for all exponents? Thanks.

II · Posted: Mon May 12, 2008 12:08 pm Post subject:

Stuart Kovinsky · Posted: Mon May 12, 2008 1:19 pm Post subject:

vinviper1 · Posted: Wed May 14, 2008 8:03 am Post subject:

Thanks Stuart!