Exponents | MathHelp.com - By MathHelp.com
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| 00:0-1 | to simplify this problem . We must apply all of | |
| 00:03 | the different exponent rules that we've learned in this chapter | |
| 00:07 | . First we apply the power rule for each set | |
| 00:10 | of parentheses in the numerator to simplify negative two extra | |
| 00:15 | third Y squared . Think of why as why to | |
| 00:19 | the first and square the coefficient of negative to to | |
| 00:24 | get positive for . And multiply each of our exponents | |
| 00:29 | by two to get X to the sixth , Y | |
| 00:32 | squared . This is all multiplied by negative X . | |
| 00:37 | Y to the 4th Cube . And think of the | |
| 00:39 | negative as negative one and X as X to the | |
| 00:44 | first . So we cube are coefficient of negative one | |
| 00:49 | which is negative one times negative one times negative one | |
| 00:52 | or negative one . And multiply each of our exponents | |
| 00:58 | by three to get X to the third , Y | |
| 01:02 | to the 12 . In our denominator we take our | |
| 01:08 | coefficient of three to the fourth power , which is | |
| 01:11 | three times three times three times three or 81 And | |
| 01:17 | multiply each of the exponents by 4 to get X | |
| 01:21 | to the 8th . Why to the 20th . Next | |
| 01:27 | we apply our product rule across the numerator , multiplying | |
| 01:32 | the two coefficients , we get negative four . But | |
| 01:38 | remember that the product rule states that when multiplying powers | |
| 01:42 | that have the same base , we add their exponents | |
| 01:46 | . So we have X to the six times X | |
| 01:48 | to the third , which is actually six plus three | |
| 01:51 | Or X to the 9th . Why Square Times why | |
| 01:55 | the 12 is why the two plus 12 Or Y | |
| 01:59 | to the 14th . So we have negative four X | |
| 02:03 | . The ninth . White of the 14th over 81 | |
| 02:06 | . X to the eighth . Why to the 20th | |
| 02:11 | . Finally we apply our quotient rule and remember that | |
| 02:14 | the quotient rule states that when you're dividing powers that | |
| 02:18 | have the same base simply subtract their exponents . So | |
| 02:23 | we have our coefficients of negative 4/81 . And for | |
| 02:30 | our exes , we take 9 -8 , which is | |
| 02:34 | one . So we have X to the first or | |
| 02:37 | X . And notice that for our wise the exponent | |
| 02:42 | in the denominator is greater than the exponents in the | |
| 02:45 | numerator . In this situation we still take the difference | |
| 02:49 | between our exponents , which is six , but the | |
| 02:53 | Y to the 6th goes in the denominator of your | |
| 02:58 | answer . |
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