SOLUTION: what is the product of -6x3 and 2x5

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Question 618712: what is the product of -6x3 and 2x5
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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You will need to use exponent rules to solve this problem. When you multiply two exponential expressions you add the exponents.
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We need to deal with the coefficients and variables separately. Let's start with the coefficients, -6 and 2. When we multiply these together we get -12. This gives us,
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%28-6x%5E3%29%282x%5E5%29=-12%2A%28x%5E3%29%28x%5E5%29
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Now we multiply the variables. "x-cubed" times "x to the fifth power" is "x to the eighth power" since 3+5 is 8. So,
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-12%2A%28x%5E3%29%28x%5E5%29=-12x%5E8
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You might be wondering how this "add the exponents when you multiply" rule works. Check this out...
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x%5E3=x%2Ax%2Ax
x%5E5=x%2Ax%2Ax%2Ax%2Ax
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When we multiply them together, we have eight factors of x, so
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%28x%5E3%29%28x%5E5%29=x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax=x%5E8
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Hope that helps. Feel free to email me at math.in.the.vortex@gmail.com if you have any questions about this.
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Ms.Figgy