How do you simplify #(x^3y^3*x^3)/(4x^2)# and write it using only positive exponents?

1 Answer
Feb 10, 2017

First, rewrite the numerator and use this rule for exponents to simplify the numerator:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))#

#(x^color(red)(3) * x^color(blue)(3) * y^3)/(4x^2) = (x^(color(red)(3) +color(blue)(3)) * y^3)/(4x^2) = (x^6y^3)/(4x^2)#

Now, we can use this rule for exponents to simplify the #x# terms in the numerator and denominator:

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

#(x^color(red)(6)y^3)/(4x^color(blue)(2)) = (x^(color(red)(6)-color(blue)(2))y^3)/4 = (x^4y^3)/4#