### Video Transcript

If π is nonzero and π over π equals π over π which equals π over π which equals π, which of the following is equivalent to πππ over πππ? Is it (A) three π cubed, (B) π cubed, (C) π, or three π?

Weβre told a relationship between π, π; π, π; and π, π. Weβre told that π and π are in the same proportion as π and π as are π and π and this proportion is equal to π. And so, letβs remind ourselves how to multiply fractions. When we multiply a pair of fractions for instance, we multiply their numerator and then separately multiply their denominators. By thinking about the reverse of that process and extending it to more than two fractions, we can say that π over π times π over π times π over π must be equal to πππ over πππ. And thatβs great because we know that each of these fractions individually is equal to π. So, we can write πππ over πππ as π times π times π.

Now, of course, π times π times π is π cubed. So, given that π is a nonzero and π over π equals π over π which equals π over π which equals π, then we know the expression thatβs equal to πππ over πππ is π cubed. In this case, thatβs option (B).