yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Simplifying quotient of powers (rational exponents) | Algebra I | High School Math | Khan Academy


2m read
·Nov 11, 2024

So we have an interesting equation here, and let's see if we can solve for K. We're going to assume that m is greater than zero, like always. Pause the video, try it out on your own, and then I will do it with you.

All right, let's work on this a little bit. You could imagine that the key to this is to simplify it using our knowledge of exponent properties. There's a couple of ways to think about it. First, we can look at this rational expression here: m to the 7/9 power divided by m to the 1/3 power.

And the key realization here is that if I have x to the a over x to the b, that this is going to be equal to x to the a minus b power. It actually comes straight out of the notion that x to the a over x to the b is the same thing as x to the a times 1/x to the b, which is the same thing as x to the a times 1/x to the b.

That's the same thing as x to the b, which is going to be the same thing as if I have a base to one exponent times the same base to another exponent. That's the same thing as that base to the sum of the exponents a plus b, which is just going to be a minus b. So we got to the same place.

So we can rewrite this as... So we can rewrite this part as being equal to m to the 7/9 power minus 1/3 power is equal to m to the K/9. And I think you see where this is going. What is 7/9 minus 1/3? Well, 1/3 is the same thing, if we want to have a common denominator, as 3/9.

So I can rewrite this as 3/9. So 7/9 minus 3/9 is going to be 4/9. So this is the same thing as m to the 4/9 power is going to be equal to m to the K/9.

So 4/9 must be the same thing as K/9. So we can say 4/9 is equal to K/9, which tells us that K must be equal to 4, and we're all done.

More Articles

View All
The Unsung Heroes of the Arctic - Ep. 3 | Wildlife: The Big Freeze
[Bertie] Polar bears are such icons of the Arctic. It’s hard for anything else to escape their shadow. But what if I told you only a few inches from the ground, there’s a host of less celebrated little creatures who’ve made a playground of these brutal co…
Travel INSIDE a Black Hole
Hey, Vsauce. Michael here. And today we are going to go inside a black hole. It’s not going to be comfortable, but it will be pretty fun. Now, first thing’s first: mathematically speaking, anything could become a black hole if you were to compress it int…
The Shark Immune System | When Sharks Attack
[music playing] NARRATOR: As experts begin to search for other explanations, they turn their attention to a series of disturbing discoveries that occurred in the months following the June 2012 attacks. We had some dolphins that washed up already dead. We…
Analyzing structure with linear inequalities: fruits | High School Math | Khan Academy
Shantanu bought more apples than bananas, and he bought more bananas than cantaloupes. Let A represent the number of apples Shantanu bought, let B represent the number of bananas, and let C represent the number of cantaloupes. Let’s compare the expressio…
Definite integrals intro | Accumulation and Riemann sums | AP Calculus AB | Khan Academy
What we’re going to do in this video is introduce ourselves to the notion of a definite integral. With indefinite integrals and derivatives, this is really one of the pillars of calculus. As we’ll see, they are all related, and we’ll see that more and mor…
Will The Market Crash If Trump Loses?! #shorts
What Donald Trump has said, if he loses, is that there’ll be a depression, that there’ll be a market crash. What do you think of that? Ah, Donald being the Donald, you got to vote one way or the other based on policy because both sides are being absolutel…