How do you simplify #\frac { 56y z ^ { 3} } { 24y ^ { 5} z ^ { 3} }#?

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Answer 1 · 2017-07-30T22:59:47

See a solution process below:

First, rewrite the expression as:

#56/24(y/y^5)(z^3/z^3) => 56/24(y/y^5)1 =>#

#56/24(y/y^5) => (8 xx 7)/(8 xx 3)(y/y^5) =>#

#(color(red)(cancel(color(black)(8))) xx 7)/(color(red)(cancel(color(black)(8))) xx 3)(y/y^5) =>#

#7/3(y/y^5)#

We can now use these rules for exponents to simplify the #y# term:

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

#7/3(y/y^5) => 7/3(y^color(red)(1)/y^color(blue)(5)) => 7/3(1/y^(color(blue)(5)-color(red)(1))) =>#

#7/3(1/y^4) =>#

#7/(3y^4)#