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: $color(green)(1/(9y^4))$

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$color(blue)("Putting it all together")$

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

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

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

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 $x/x=1$

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

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

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