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OpenStudy (anonymous):

how to simplify: 4A^4B^2C^6/12A^2B^-5C^8

OpenStudy (anonymous):

\[4A^2B^2C^6/12A^2B^-5C^8\]

OpenStudy (anonymous):

You simplify piece by piece. Look at the 4 and the 12, you can reduce that to 1 and 3. Then cross off for each letter, the smaller exponent (either top or bottom) and subtract from the same letter's exponent on the other side. So you get \[(4A^{4}B^{2}C^{6})/(12A^{2}B^{-5}C^{8}) = (A^{2}B^{7})/(3C^{2})\] Note that when you subtracted the B exponent, -5 is the smaller and 2-(-5) = 7.

OpenStudy (anonymous):

alright thanks so much for your help. !=] i have a test tomorrow and i would like to gets some help on it, i have another question how would you simplify \[7/\sqrt{11}\]

OpenStudy (anonymous):

To simplify a radical on the bottom, multiply both the top and the bottom by the radical (essentially multiplying by 1). This will clear the radical because you're multiplying it by itself (squaring a square root). This would give you \[7\sqrt{11}/11.\] Since the square root of 11 cannot be simplified, this is as far as you can go.

OpenStudy (anonymous):

thanks, i really appreciate your help

OpenStudy (anonymous):

my pleasure

OpenStudy (anonymous):

how would you find the product: \[x^2+5x+4/x^2+2x+1\times2x+2/x+4\]... can you help me on this one.

OpenStudy (anonymous):

You probably are already familiar with FOIL (First, Outer, Inner, Last), but that only works with binomials (statements with two terms). But the main idea behind FOIL is that you are distributing *all* of the terms of one statement across the other statement. You then combine like terms to simplify. So I'm going to rewrite the problem switching the factor \[(2x +2/x +4)(x^{2}+7x+4/x^{2} +1)\] Note, I combined the 5x and the 2x into 7x because they are already like terms. At this point, you distribute each term of the first statement with the entire second statement. This gives you \[2x(x^{2}+7x+4/x^{2}+1)+(2/x)(x^{2}+7x+4/x^{2}+1)+4(x^{2}+7x+4/x^{2}+1)\]\[ =2x^{3}+14x^{2}+8/x+2x+2x+14+8/x^{3}+2/x+4x^{2}+28x+16/x^{2}+4\] Now go through and combine anything that is the same (i.e. x-cubes, x-squares, etc.) Do not, however, get confused and think that \[2x^{3}\] and \[8/x^{3}\] are like terms...they are not. The second one is 8 divided by the x-cubed and since that puts the x on the bottom, it is not the same exponent (the real exponent of that is -3)

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