How do you simplify #\frac { 4x ^ { 3} y ^ { 5} } { 8x ^ { 7} y ^ { - 2} }#?

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Answer 1 · 2017-06-04T00:07:58

See a solution process below:

First, rewrite the expression as:

#(4/8)(x^3/x^7)(y^5/y^-2) => 1/2(x^3/x^7)(y^5/y^-2)#

Next, we will use this rule of exponents to simplify the #x# term:

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

#1/2(x^color(red)(3)/x^color(blue)(7))(y^5/y^-2) => 1/2(1/x^(color(blue)(7)-color(red)(3)))(y^5/y^-2) =>#

#1/2(1/x^4)(y^5/y^-2) => 1/(2x^4)(y^5/y^-2)#

Now, use this rule of exponents to simplify the #y# term:

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

#1/(2x^4)(y^color(red)(5)/y^color(blue)(-2)) => 1/(2x^4)(y^(color(red)(5)-color(blue)(-2))) => 1/(2x^4)(y^(color(red)(5)+color(blue)(2))) =>#

#1/(2x^4)(y^7) => y^7/(2x^4)#