WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; this lesson is on the introduction of exponents.
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When you have a number with an exponent, that number, this number right here, 10, is called the base.
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This 2 is called the exponent.
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This can be read as 10 squared, or 10 to the power of 2, or 10 to the 2nd power.
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Whenever you have a base with a number that is a little bit higher to the side of it,
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then that is called the exponent; you read it 10 to the power of 2.
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Or if it is a 2, then you can just say 10 squared.
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Find the value of 6 to the 3rd power.
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Exponent, what that means is you are saying that 6 is going to be a factor 3 times.
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When we have 6 to the 3rd power, we are going to write this out as 6 times 6 times 6.
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It is just this number multiplied by itself that many times.
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Be careful; this is not 6 times 3; this is not 18.
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We have to write this out as 6 times 6 times 6; then you just solve this out.
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We have 6 times 6 is 36; we have to multiply that by 6 again.
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If you do 36 times 6, then you are going to get 6 times 6, 36.
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This is 18; plus the 3 is 21; 6 to the 3rd power is 216.
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Another example, this is written out in expanded form.
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It is 4 times 4 times 4 times 4 times 4.
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When we write that in exponent form, we are going to write the 4 as a base
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because all these numbers are 4s so the base is going to be a 4.
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How many times did it multiply by itself?
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1, 2, 3, 4, 5; there is 5 of them.
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I am going to write that as my exponent.
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It is going to be 4 to the 5th power.
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4 to the power of 5 or 4 to the 5th power.
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Write 125 using an exponent and the base 5.
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That means we want the base to be a 5.
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We are going to have to see what the exponent is going to be
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so that when we solve that out, it is going to become 125.
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Base is 5.
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Again I need to find a number that goes there as my exponent
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so that when I solve this out, it is going to become 125.
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First, in order for me to do this, I have to see
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how many times I have to multiply 5 to itself to get 125.
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125 is going to be... this is called the factor tree.
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We haven't gone over that yet; it is later on in the lesson.
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But we are just going to break this up; 125 is 25 times 5.
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25 times 5 is 125; this 25 is 5 times 5.
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That means 5 times 5 times this 5 gives you 125.
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This can be written out as 5 times 5 times 5.
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5 times 5 is 25; 25 times 5 is 125.
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To write this using base 5, my exponent is going to be... how many times did I multiply 5 to itself?
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3 times; it is going to be 3.
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My answer is 5 to the 3rd power.
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The next example, write the equal factors and the value of 3 to the 4th power.
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The equal factors just means for you to write it out in expanded form.
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It is 3 times 3 times 3 times 3.
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Again, whenever you are solving exponents, make sure you write it out like this so you don't multiply 3 times 4.
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This is not 12; be careful with that.
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Exponents tell you how many times you are going to multiply this base number to itself.
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We are going to multiply 3 to itself 4 times.
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It is 3 times 3 times 3 times 3.
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When I multiply this out, I can multiply these two first.
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This is going to be 9; we can multiply these two; that is 9.
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9 times 9 is 81; 3 to the 4th power is 81.
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That is it for this lesson on exponents; thank you for watching Educator.com.