Exponents, Value of N

[ornelaspedro]

IF 5^21 x 4^11 = 2 x 10^n what is the value of n?

11
21
22
23
32

The answer is 21 could somebody explain why?

[DanaJ]

This question has been answered many times before. But here goes:

10^n = (2*5)^n = (2^n)*(5^n). This means that:

2 * 10^n = 2*(2^n)*(5^n) = [2^(n+1)]*(5^n).

Now, look at the left side: 4^11 = (2^2)^11 = 2^22.

So you have:

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

This is why n = 21.