Exponent Time 2 (GPREP)

zagcollins wrote:5^21*4^11=2*10^n Find value of n

Cant remember the answer options as usual..

Let's make the left side look like the right side.

5^21*4^11
5^11 * 5^10 * (2*2)^11
5^11 * 5^10 * 2^11 * 2^11
(5^11 * 2^11) * (5^10 * 2^10) * 2^1
(5*2)^11 * (5*2)^10 * 2
10^11 * 10^10 * 2
10^(10+11) * 2
10^21 * 2 = 2*10^21
n = 21

We also could have started by dividing both sides by 2, to get:

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

and solved from there - this way the extra "2" would have cancelled out earlier, so we'd eventually get:

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

and proceed from there to end up with:

10^21 = 10^n