gmat prep exponent question

[xcise_science]

Someone posted this question before, but I can't find it on the forums, can someone explain it?

5^21*4^11=2(10^n), what is n?


Thanks

[syv11]

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

[xcise_science]

thanks, but how did you get from here:
5^21*2^22=2*10^n to
5^21*2^21=10^n

[sujaysolanki]

2^22 - 2^1 is what being used ...
that gives 2^21 ..then the powers can be combined a ^x * b ^ x = ab ^x
hope that helps

[xcise_science]

oh, ok, so you subtracted 2 from both sides?
I didn't see that before.

Thanks!

[syv11]

You need to devide it by 2! Not substract!

2^22/2 = 2^(22-1) = 2^21