How do you simplify #(9 sqrt(50x^2)) / (3 sqrt(2x^4))#?

1 Answer
Apr 14, 2016

Answer:

#15/x#

Explanation:

#1#. Start by factoring out #3# from the numerator and denominator.

#(9sqrt(50x^2))/(3(sqrt(2x^4))#

#=(3(3sqrt(50x^2)))/(3(sqrt(2x^4)))#

#=(3sqrt(50x^2))/(sqrt(2x^4))#

#2#. Multiply the numerator and denominator by #sqrt(2x^4)# to get rid of the radical in the denominator.

#=(3sqrt(50x^2))/(sqrt(2x^4))((sqrt(2x^4))/(sqrt(2x^4)))#

#3#. Simplify.

#=(3sqrt(100x^6))/(2x^4)#

#=(3*10sqrt(x^6))/(2x^4)#

#=(3*5x^(6(1/2)))/x^4#

#=(15x^3)/x^4#

#3#. Use the exponent quotient law, #color(purple)b^color(red)m-:color(purple)b^color(blue)n=color(purple)b^(color(red)m-color(blue)n)#, to simplify #x^3/x^4#.

#=15x^(3-4)#

#=15x^-1#

#=color(green)(|bar(ul(color(white)(a/a)15/xcolor(white)(a/a)|)))#