SOLUTION: simplify: 16x^5y^4 over 32xy^7

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 Click here to see ALL problems on Expressions-with-variables Question 65366: simplify: 16x^5y^4 over 32xy^7 Answer by Edwin McCravy(8880)   (Show Source): You can put this solution on YOUR website!``` 16x5y4 32xy7 Give the exponent 1 to the letter x in the bottom 16x5y4 32x1y7 Cancel the 16 and the 32, putting 2 below the 32 since 32÷16 = 2, and putting 1 above the 16, since 16÷16 = 1 1 16x5y4 32x1y7 2 So now you have 1x5y4 2x1y7 Now use the rule for subtracting exponents: When two exponential with the same base appear as a factor of the numerator and the denominator: Subtract the smaller exponent from the larger exponent and place (a) the resulting exponent with the common base in the numerator if that's where the larger exponent was previously and eliminate it from the denominator. Or, (b) the resulting exponent with the common base in the denominator if that's where the larger exponent was previously and eliminate it from the numerator. So here we have a case of each 1x5y4 2x1y7 We subtract the exponent of x1 from the exponent of x5, and get x4, and we place x4 in the numerator because the larger exponent 5 was in the numerator, and we eliminate x from the denominator: 1x4y4 2y7 We subtract the exponent of y4 from the exponent of y7, and get y3, and we place y3 in the denominator because the larger exponent 7 was in the denominator, and we eliminate y from the numerator: 1x4 2y3 Now we can erase the 1 coefficient in the top x4 2y3 Edwin```