SOLUTION: Simplify: {{{(19x^3y^4z^5)/(9xy^3z^2)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify: {{{(19x^3y^4z^5)/(9xy^3z^2)}}}      Log On


   

Question 136222: Simplify: %2819x%5E3y%5E4z%5E5%29%2F%289xy%5E3z%5E2%29
Found 2 solutions by Edwin McCravy, ky_mathemagician:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
19x^3y^4z^5 DIVIDED BY 9xy^3z^2
%2819x%5E3y%5E4z%5E5%29%2F%289xy%5E3z%5E2%29
Write every base as a multiplier as many times as the exponent:
%2819xxxyyyyzzzzz%29%2F%289xyyyzz%29
Put parentheses around each factor

Cancel whatever will cancel between numerator and denominator

Eliminate what canceled
%28%2819%29%28x%29%28x%29%28y%29%28z%29%28z%29%28z%29%29%2F%28%289%29%29
Take away the parentheses
%2819xxyzzz%29%2F9
Write as exponents
%2819x%5E2yz%5E3%29%2F9
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Shorter way:
Give the x in the bottom the exponent 1
%2819x%5E3y%5E4z%5E5%29%2F%289x%5E1y%5E3z%5E2%29
Subtract exponents and eliminate the one with the
smaller exponent:
%2819x%5E%283-1%29y%5E%284-3%29z%5E%285-2%29%29%2F9
Simplify
%2819x%5E2y%5E1z%5E3%29%2F9
Erase the 1 exponent:
%2819x%5E2yz%5E3%29%2F9
Edwin

Answer by ky_mathemagician(1) About Me  (Show Source):
You can put this solution on YOUR website!
Using the exponent rule , %28x%5Em%29%2F%28x%5En%29+=+x%5E%28m-n%29, we have
%28%2819x%5E%283-1%29y%5E%284-3%29z%5E%285-2%29%29%2F%289%29%29 =
%28%2819x%5E2yz%5E3%29%2F%289%29%29 .