- #1

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^{2 }and x

^{5}, we get x

^{7}. Quick, dumb question:

Why isn't it x

^{10}instead (since we're multiplying and not adding)?

- Thread starter pandaexpress
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- #1

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Why isn't it x

- #2

jedishrfu

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- #3

Mark44

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##x^2## means ##x \cdot x##, and ##x^2## means ##x \cdot x \cdot x \cdot x \cdot x##, so ##x^2 \cdot x^5## means ##x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x##, right? How many factors of x are there in that last expression?^{2 }and x^{5}, we get x^{7}. Quick, dumb question:

Why isn't it x^{10}instead (since we're multiplying and not adding)?

- #4

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This might seem a little dumb, but I figured that multiplying would give youmultipliedtogether gives you 7 x's or x^7

x

x

Wouldn't x

x*x*x*x*x; x*x*x*x*x Or, in other words, two groups of x*x*x*x*x.

It's the same idea with regular multiplication, where if you have 2X5, then it's like

|| || || || || (five groups of two) or |||||; ||||| (two groups of five)

I just don't quite understand why we're adding and getting 7 (instead of 10), since the operation is to

If they want you to add the exponents, then why not just say x

- #5

Mark44

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No.This might seem a little dumb, but I figured that multiplying would give you^{10}still. Using your example above,

x^{2}= x*x

x^{5}= x*x*x*x*x

Wouldn't x^{2}* x^{5}= x*x; x*x; x*x; x*x; x*x?

What you have written is ##(x^2)^5##, or 5 factors of ##x^2##, making 10 factors of x, or ##x^{10}##.

With ##(x^2) \cdot (x^5)## you have two factors of x multiplying 5 factors of x, making 7 factors of x, or ##x^7##.

No, again. The operation is to multiply ##x^2## and ##x^5##, which results in the exponents beingpandaexpress said:Basically, you'd have a pair of x*x's five times. Or, you would get:

x*x*x*x*x; x*x*x*x*x Or, in other words, two groups of x*x*x*x*x.

It's the same idea with regular multiplication, where if you have 2X5, then it's like

|| || || || || (five groups of two) or |||||; ||||| (two groups of five)

I just don't quite understand why we're adding and getting 7 (instead of 10), since the operation is tomultiplyexponents.

Because the terms in ##x^2 + x^5## are not like terms (i.e., same exponent), they can't be combined.pandaexpress said:Do you guys see what I mean?

If they want you to add the exponents, then why not just say x^{2}+ x^{5}?

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