### Video Transcript

If nine to the power of π₯ equals four and nine over nine to the power of π¦ equals five, what is the value of nine to the power π₯ plus π¦?

In this question, we have two separate equations. And weβre asked to find the value of one term, nine to the power of π₯ plus π¦. We can see in these equations that weβre given that we do have something similar to nine to the power of π₯ plus π¦. In the first equation, weβre told nine to the power of π₯. And in the second equation, thereβs a nine to the power of π¦. So letβs see if we can rearrange them and join the equations together.

To do this, weβre going to need to remember our rules of exponents. In particular, the rule π₯ to the power of π times π₯ to the power of π equals π₯ to the power of π plus π. If we take a closer look at our term, nine to the power of π₯ plus π¦, we can see that itβs very similar to the term weβve got in the rules of exponents, the π₯ to the power of π plus π.

Since π₯ to the power of π plus π is equal to two terms, π₯ to the power of π times π₯ to the power of π, then we can say that nine to the power of π₯ plus π¦ is also equal to nine to the power of π₯ times nine to the power of π¦. If we look at the equations weβre given, we can see that we do have an equation thatβs equal to nine to the power of π₯. But we donβt yet have an equation thatβs equal to nine to the power of π¦.

So letβs take our second equation and see if we can rearrange it so that nine to the power of π¦ is the subject of our equation. To start by rearranging our equation nine over nine to the power of π¦ equals five, we want to move nine to the power of π¦ from being on the denominator. And we can do this by multiplying both sides of our equation by nine to the power of π¦. This will give us nine equals five times nine to the power of π¦. And next, to find nine to the power of π¦ by itself, we need to divide both sides of our equation by five, giving us nine over five equals nine to the power of π¦.

So now we have the equations nine to the power of π₯ equals four and nine to the power of π¦ equals nine over five. We can substitute these into our equation nine to the power of π₯ plus π¦ equals nine to the power of π₯ times nine to the power of π¦. This will give us nine to the power of π₯ plus π¦ equals four times nine over five. And we can simplify the numerical values on the right-hand side to give us nine to the power of π₯ plus π¦ equals 36 over five.