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# Algebra Dividing and Exponents

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### Algebra Dividing and Exponents

1. 1. Image Source: http://chrome.brainpop.com
2. 2. We first need to look at how to break numbers down intotheir lowest “Prime Factors” (eg. 2, 3, 5, 7, 11, 13, etc)The easiest way to do this is to make a “Factor Tree”,where the prime number factors end up as the outer leavesof our tree. 12 2 x 6 2 x 3 12 = 2 x 2 x 3
3. 3. 16 92 x 8 3 x 3 2 x 4 9=3x3 2 x 2 16 = 2 x 2 x 2 x 2 6We will be using Prime Factors 2 x 3for Reducing down NumberFractions in our Expressions 6=2x3
4. 4. To Divide Algebra Exponents Terms, follow these steps: Write any question as a Fraction Break Numbers into their Lowest Prime Factors Expand out fully all Powers Exponents Terms Cancel all identical Top and Bottom items Write Final Answer as a Fraction without x signs
5. 5. 12 6 Rewrite as a Fraction= 12 Write Numbers as Prime Factors 6= 2x2x3 and then cancel all identical 2x3 items in the top and bottom= 2
6. 6. 12w 6 Rewrite as a Fraction= 12w Write Numbers as Prime Factors 6 and Expand all letter Variables= 2x2x3xw and then cancel all identical 2x3 items in the top and bottom= 2w Answer = Remaining items
7. 7. 12ab 16b Rewrite as a Fraction= 12ab Write Numbers as Prime Factors 16b and Expand all letter Variables= 2x2x3xaxb and cancel all identical 2x2x2x2xb items in top and bottom= 3a Use remaining items 4 to form the answer
8. 8. 12a2b3 9ab5 Rewrite as a Fraction= 12a2b3 Write Numbers as Factors 9ab5 and Expand all Powers Terms= 2x2x3xaxaxbxbxb Cancel 3x3xaxbxbxbxbxb Items= 4a Use remaining items 3b2 to form the answer
9. 9. -2a3b2 6a4b Rewrite as a Fraction= -2a3b2 Write Numbers as Factors 6a4b and Expand Powers Terms= -2 xaxaxaxbxb Cancel Items 2x3xaxaxaxaxb but do not cancel the= -b minus sign 3a
10. 10. -eh - 8eh Rewrite as a Fraction= -eh Write Numbers as Factors -8eh and Expand all Variables= -e xh Cancel Items -2 x 2 x 2 x e x h including cancelling the minus signs= = 1 8 8 Fill empty top with a 1