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When multiplying x2 and x5, we get x7. Quick, dumb question:
Why isn't it x10 instead (since we're multiplying and not adding)?
Why isn't it x10 instead (since we're multiplying and not adding)?
##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?When multiplying x2 and x5, we get x7. Quick, dumb question:
Why isn't it x10 instead (since we're multiplying and not adding)?
This might seem a little dumb, but I figured that multiplying would give you 10 still. Using your example above,Think of the exponent as counting the number of factors so x^2 is x*x and x^5 is x*x*x*x*x and when multiplied together gives you 7 x's or x^7
No.This might seem a little dumb, but I figured that multiplying would give you 10 still. Using your example above,
x2 = x*x
x5 = x*x*x*x*x
Wouldn't x2 * x5 = x*x; x*x; x*x; x*x; x*x?
No, again. The operation is to multiply ##x^2## and ##x^5##, which results in the exponents being added.pandaexpress 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 to multiply exponents.
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 x2 + x5?