00:01
All right, we're on question 298, and we're asked to solve for x.
00:05
So it says 625 times 5 to the 3x plus 3 is equal to 125.
00:12
Thinking about the properties we use on the previous problems, we want to be able to simplify this.
00:22
I could potentially divide both sides by 625, but i think i'm going to be able to break this down to 5 to an exponent.
00:32
And if i'm able to do that, then i can use this rule over here, a to the n times a to the n is equal to a to the n plus n.
00:41
As long as my bases are the same, i would be able to multiply the exponent or multiply factors together and add the exponent.
00:48
So let's give that a try.
00:50
Let's use prime factorization to break down our 625.
00:56
So i can clearly see that 625 is divisible by 5.
01:01
So that is helpful.
01:04
So let's start with 5 times 125.
01:15
Okay, 5 is prime.
01:17
So let's leave that.
01:19
And 125 is going to be 5 times 25.
01:27
And lastly, we have 25 is 5 times 5.
01:33
So what this means is i can actually rewrite 525 as 5 to the fourth power...