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We see "5" and "4" on the left side and "10" on the right side.. somehow we want to make the bases the same.

So, let's start by turning the "4" into "2^2":

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

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

Now, we want to be able to simplify the left side, but we can only do so if the exponents are equal, so:

(5^21)(2^21)(2^1) = 2*10^n

if we divide both sides by 2, we get:

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

and since the exponents are equal on the left side, we can say:

(5*2)^21 = 10^21

and finally

10^21 = 10^n

so 21 = n.

Not a difficult one i guess.....

Lets break it into prime factors...

(5^21)(4^11)=2x10^n

5^21*(2^2)^11=2*(2.5)^n

5^21*2^22 = 2*2^n.5^n

5^21*2^22 = 2^(n+1).5^n

Either equate exponents of 2 or 5. Both gives n = 21.

_________________
Shalabh Jain,
e-GMAT Instructor