How do you simplify #\frac { 72x ^ { 5} y ^ { 8} z ^ { 5} } { - 12x y ^ { 2} z ^ { 3} }#?

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Answer 1 · 2017-08-08T20:42:51

See a solution process below:

First, rewrite the expression as:

#(72/-12)(x^5/x)(y^8/y^2)(z^5/z^3) =>#

#-6(x^5/x)(y^8/y^2)(z^5/z^3)#

Now, rewrite the denominator for the #x# term using this rule of exponents:

#a = a^color(blue)(1)#

#-6(x^5/x^color(blue)(1))(y^8/y^2)(z^5/z^3)#

Now, use this rule of exponents to simplify each of the variable terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#-6(x^color(red)(5)/x^color(blue)(1))(y^color(red)(8)/y^color(blue)(2))(z^color(red)(5)/z^color(blue)(3)) =>#

#-6x^(color(red)(5)-color(blue)(1))y^(color(red)(8)-color(blue)(2))z^(color(red)(5)-color(blue)(3)) =>#

#-6x^4y^6z^2#