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

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

5^21*2^21=10^n

(10)^21=10^n

n=21

The basic rule here is that when you calculate the x-root of a base, you then multiply the exponent by x.

For example:

8^2 = 2^6 = 64
Here, you can see that 2 is the cube root of 8. Since a number cubed is a number raised to the 3rd power, you multiply the old exponent (2) from the old base (8) by 3.

9^3 = 3^6 = 729

16^2 = 4^4