WEBVTT
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Let’s talk about powers and exponents.
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Unfortunately, for this stickman superhero, we’re not talking about those kind of powers.
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When I say the word “powers,” I mean numbers that are expressed with exponents.
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Powers are numbers expressed using exponents.
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Okay, so let’s look at this.
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32 equals two times two times two times two times two.
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Or another way we write that is two to the power of five.
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Every power is made up of two components.
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The two here in the green is called the base.
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And the five, the smaller number at the top of the base, is called the exponent that you see in yellow here.
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The two components together are then called a power.
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Not only is two to the fifth a power, it’s also something that we call exponential form.
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When we’re working with exponents, the exponent tells us how many times to multiply the base by itself.
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So in our last example, the base was two and the exponent was five.
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That meant that we needed to take the base of two and multiply it by itself five times.
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Two times two times two times two times two, which equals 32.
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So when we see seven to the fourth power, what does that mean?
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Our exponent here is four and the base is seven.
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So we know we’re gonna multiply seven by itself four times, seven times seven times seven times seven.
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There’s a name that we use when we write out our exponents in the form like this.
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We call it standard form.
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In this case, seven to the fourth power is 2401.
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Seven to the fourth power equals 2401.
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And here you can see that seven to the fourth power we call a power.
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Or we say that it’s written in exponential form.
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We have the standard form, which is where we write seven as a product of seven times seven times seven times seven.
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And then the solution is there.
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There’s one more thing we need to talk about.
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And that’s the words we use when we’re talking about powers.
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In the last example, I called this seven to the fourth power.
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That’s the words I used, seven to the fourth power.
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But some powers are special.
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And we use different words.
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While it is true that this is five to the second power, we actually call it five squared.
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Anytime you’re dealing with powers and the exponent is two, that number is called “squared,” just like in our example here, five squared.
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The other special case power is when we have a power of three.
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Anytime we have a power of three, we use the word “cubed.”
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So this one, four to the third power, we would say four cubed instead.
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So let’s try and write these powers in standard form.
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Standard form means we wanna write these without their exponents.
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Three to the fifth power looks like this, and five squared is written like this.
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And another example, we wanna write these values in exponential form.
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So let’s use exponents to simplify these values and write them as a base and an exponent.
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Here we have seven multiplied by itself three times, so that’s seven cubed.
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10 is being multiplied by itself four times.
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And we write that as 10 to the fourth power.
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Now you can go try out your powers and exponents powers for yourself.