First notice that 4 = 2^2DCS80 wrote:9) If m and n are positive integers and (2^18)(5^m) = (20^n), what is the value of m?
Also notice that 20^n = (4x5)^n = (4^n)(5^n)
So, we can take (2^18)(5^m) = (20^n) and rewrite it as:
[(2^2)^9][5^m] = [4^n)(5^n)
[4^9][5^m] = (4^n)(5^n)
From this, we can see that m=n (since 5^m must equal 5^n)
And we can see that n = 9, (since 4^9 must equal 4^n)
So, we get n = m = 9
So, [spoiler]m = 9[/spoiler]
Cheers,
Brent
