# Question Video: Simplifying Algebraic Fractions Mathematics • 10th Grade

Find the quotient of (26πβ·πβ΅ β 9πΒ³πβ΅)/πΒ²π.

02:35

### Video Transcript

Find the quotient of 26 π to the power of seven π to the power of five minus nine π cubed π to the power of five all over π squared π.

In order to actually solve this problem, what I wanna do is I actually want to break it into two parts. And we can actually do it using this relationship here, that says that π plus π over π is equal to π over π plus π over π.

And we can actually use that to split our question into two parts. Because we can actually say that our expression is equal to 26 π to the power of seven π to the power of five over π squared π plus negative nine π cubed π to the power of five over π squared π. Okay, great!

So now weβve got this, weβre actually going to simplify in two parts. And to enable us to actually simplify these different parts Iβve split it into. Weβre actually gonna use one of our exponent rules. And this rule states that π to the power of π divided by π to the power of π is equal to π to the power of π minus π.

So if weβre actually dividing two terms, where theyβre the same term, then actually what we can do is subtract the powers. So letβs go ahead and use this over here. So first of all, Iβm gonna have 26 and then π to the power of seven minus two because seven would be like our π and two would be like our π in our exponent rule. And then we get π to the power of five minus one.

And thatβs, again, because our five is like our π and then our one will be like our π. And thatβs just remembering that when itβs just π on its own, itβs like π to the power of one. So great! And now we can actually fully simplify the left-hand side, which leaves us with 26 π to the power of five π to the power of four. Great! So now letβs get on to the right-hand side.

So first of all, weβre gonna get negative nine π to the power of three minus two. And then weβve got π to the power of five minus one. So great! Now we can fully simplify this. So that means our right-hand side, fully simplified, is negative nine ππ to the power of four. So great! Final thing we need now to know is to bring it all together.

So it says this is all equal to 26 π to the power of five π to the power of four plus negative nine ππ to the power of four. Then we finally tidy it up, and we can say that our final answer is that the quotient of 26 π to the power of seven π to the power of five minus nine π cubed π to the power of five over π squared π is equal to 26 π to the power of five π to the power of four minus nine ππ to the power of four.