Exponents

[nkaur]

5^21 x 4^11=?

How do I solve this type of question?

THanks a lot.

[Frankenstein]

Hi,
5^21.4^11 = 5^21.(2^2)11 = 5^21.2^22 = 2.(5.2)^21 = 2.10^21

Cheers!

[manpsingh87]

5^21 x 4^11=?

How do I solve this type of question?

THanks a lot.

always reduce the given expression into the prime factor form; 5^21x4^11= 5^21x2^22;
now we know that 5*2=10; hence it can be written as (5.2)^21*2; 2*10^21;

[Brian@VeritasPrep]

Hey nkaur,

Great question - and thanks for Frankenstein and manpsingh for terrific responses.

One more thing to add - the GMAT is great because it always comes with answer choices, so if you're ever in a position where you're stuck on how to get started on some algebra, it's usually helpful to look at the answer choices to see where they want you to go.

On a question like this, they probably want you to get to 2*10^21, but you don't have to do that on your own. You'd have answer choices like, perhaps:

A) 2*10^21
B) 20^21
C) 210^21
D) 20^31
E) 4*10^22

So there are clues - which of these can you realistically get to? If you eliminate a few that seem way, way off (C, for example) you have fewer choices and some targets for your algebra. Can you get a 20 out of that? Well, sure...if you have a common exponent, but the best you can do is (5*4)^11, because 11 is the biggest common exponent, and then you have 5^10 left. That can't get you to B or D. So you need to get a 10. How do you do that? Well, that's 5*2, so you need to break down 4^11 to 2^22 and go from there.

The beautiful thing about many algebra or exponent problems is that the answer choices give you nice clues as to what you need to do, so make it a habit to glance at the answer choices before you get started so that you have a plan for where you need to go.