SOLUTION: Simplify the following 2x^4 ۪ 5x^2 10x^7 3x^5

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Question 150977: Simplify the following
2x^4 ۪ 5x^2
10x^7 3x^5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%5E4%29%2F%2810x%5E7%29%29%28%285x%5E2%29%2F%283x%5E5%29%29 Start with the given expression.


%28%282x%5E4%29%285x%5E2%29%29%2F%28%283x%5E5%29%2810x%5E7%29%29 Combine the fractions.


%2810x%5E6%29%2F%28%283x%5E5%29%2810x%5E7%29%29 Multiply 2x%5E4 and 5x%5E2 to get %282x%5E4%29%285x%5E2%29=%282%2A5%29x%5E%284%2B2%29=10x%5E6


%2810x%5E6%29%2F%2830x%5E%2812%29%29 Multiply 3x%5E5 and 10x%5E7 to get %283x%5E5%29%2810x%5E7%29=%283%2A10%29x%5E%285%2B7%29=30x%5E%2812%29


%281%2F3%29%28x%5E6%2Fx%5E12%29 Divide the coefficients 10 and 30 to get 1%2F3


%281%2F3%29x%5E%286-12%29 When you divide monomials, simply subtract the exponents.


%281%2F3%29x%5E%28-6%29 Subtract.


%281%2F3%29%281%2Fx%5E6%29 Rewrite x%5E%28-6%29 as 1%2Fx%5E6


1%2F%283x%5E6%29 Combine the fractions.


So %28%282x%5E4%29%2F%2810x%5E7%29%29%28%285x%5E2%29%2F%283x%5E5%29%29 simplifies to 1%2F%283x%5E6%29.


In other words, %28%282x%5E4%29%2F%2810x%5E7%29%29%28%285x%5E2%29%2F%283x%5E5%29%29=1%2F%283x%5E6%29 where x%3C%3E0