How do you simplify #(10x^4 y^9) /( 30x^12 y^-3)#?

1 Answer
Mar 10, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#10/30(x^4/x^12)(y^9/y^-3) =>#

#(1color(red)(cancel(color(black)(0))))/(3color(red)(cancel(color(black)(0))))(x^4/x^12)(y^9/y^-3) =>#

#1/3(x^4/x^12)(y^9/y^-3)#

Next, use this rule for exponents to simplify the #x# term:

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

#1/3(x^color(red)(4)/x^color(blue)(12))(y^9/y^-3) =>#

#1/3(1/x^(color(blue)(12)-color(red)(4)))(y^9/y^-3) =>#

#1/3(1/x^8)(y^9/y^-3) =>#

#1/(3x^8)(y^9/y^-3)#

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

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

#1/(3x^8)(y^color(red)(9)/y^color(blue)(-3)) =>#

#1/(3x^8)(y^(color(red)(9)-color(blue)(-3))) =>#

#1/(3x^8)(y^(color(red)(9)+color(blue)(3))) =>#

#1/(3x^8)(y^12) =>#

#y^12/(3x^8)#