How do you simplify #\frac { 2x ^ { 3} y ^ { - 2} z ^ { - 4} } { 6y }#?

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Answer 1 · 2018-06-22T14:44:14

See a solution process below:

First, we can rewrite the expression as:

#(2x^3z^-4)/6(y^-2/y) =>#

#(x^3z^-4)/3(y^-2/y)#

Next, use this rule for exponents to eliminate the negative exponent for the #z# term:

#x^color(red)(a) = 1/x^color(red)(-a)#

#(x^3z^color(red)(-4))/3(y^-2/y) =>#

#x^3/(3z^color(red)(- -4))(y^-2/y) =>#

#x^3/(3z^4)(y^-2/y)#

Now, use these rules of exponents to simplify the #y# terms:

#a = a^color(blue)(1)# and #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#x^3/(3z^4)(y^-2/y) =>#

#x^3/(3z^4)(y^color(red)(-2)/y^color(blue)(1)) =>#

#x^3/(3z^4)(1/y^(color(blue)(1)-color(red)(-2))) =>#

#x^3/(3z^4)(1/y^(color(blue)(1)+color(red)(2))) =>#

#x^3/(3z^4)(1/y^3) =>#

#x^3/(3y^3z^4)#