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Find the volume of a cube with a side length of 8xy squared.

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So we have a cube right here.

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And they're saying that each of the sides, for a cube all

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the sides have the same length, each of them have

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length 8xy squared.

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So the length of this side, maybe we call this the width,

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is 8xy squared.

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The length of this side, maybe we can call that the depth, or

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the length, depending on how you want to

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label it, is 8xy squared.

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The height of this cube is also going to be 8xy squared.

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A cube, all of the dimensions are the same.

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Now, if you want to take the volume of any a rectangular

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prism, you'll multiplied these three dimensions.

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You"ll multiply the width times the

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depth times the height.

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Now, in a cube, these are all the same dimensions.

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So you can just take this dimension and multiply it by

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itself three times.

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Or you could take it to the third power.

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So the volume of this cube is 8xy squared, I could just

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multiply it by itself three times, or I could say to the

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third power.

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That's why raising something to the third power is

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called cubing it.

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Because you're essentially finding the volume of a cube,

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where the thing that you're cubing is the dimension of

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each of the sides.

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Now, what's this going to be?

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Well, when you take a product and you raise it to some

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power, that's the same thing as taking each of the terms to

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that power.

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So this is the same thing as 8 to the third power times x to

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the third power times y squared to the third power.

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And what's 8 to the third power?

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8 squared is 64, so we'll multiply 64 times 8.

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4 times 8 is 32.

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6 times 8 is 48 plus 3 is 51.

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So it's 512.

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So this is equal to 512 times x to the third and y squared

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to the third power, that's the same thing is y to the 2 times

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3 power, or y to the sixth power.

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And we're done.

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We found the volume of the cube.

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It's 512 x to the third y to the sixth.

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