How do you simplify #((2x^-1) / (3y^2)^2) times (3x^2)/(5y)#?

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Answer 1 · 2016-04-16T15:43:05

#(6x)/(45y^5)#

Every step shown to aid understanding. As you become practised you will be able to skip steps.

Splitting the given expression down into its component parts

#color(blue)("Consider "2x^(-1)#

This is another way of writing: #color(green)(2/x)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider " 1/((3y^2)^2))#

This is another way of writing: #color(green)(1/(9y^4))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#2/x xx 1/(9y^4) xx(3x^2)/(5y)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Simplifying")#

#(2xx1xx3x^2)/(x xx9y^4xx5y)#

#(6x^2)/(45xy^5)#

Separate out the #x's#

#x^2/x xx(6)/(45y^5)#

#(x xx x)/x xx(6)/(45y^5)#

#x /x xx x/1xx(6)/(45y^5)#

But #x/x=1#

#1xx x/1xx6/(45y^5)#

#(6x)/(45y^5)#