How do you multiply #(\frac { 2x } { 5} ) ^ { 2} \cdot ( \frac { 5} { x } ) ^ { 2} #?

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Answer 1 · 2017-02-22T20:30:08

#4#

Before we multiply, let's simplify each individual term.

#((2x)/5)^2 * (5/x)^2#

Each term can be simplified since they are being squared.

#((2x)/5)((2x)/5) * (5/x)(5/x)#

SImplify each term.

#((2x*2x)/(5*5)) * ((5*5)/(x*x))#

Simplify further.

#((4x^2)/25) * (25/x^2)#

Now we can multiply. Let's simplify across the numerators and denominators first.

#(4cancel(x^2))/(25) * (25)/(cancelx^2)#

Now we get:

#4/25 * 25/1#

This can still be simplified.

#4/cancel(25) * cancel(25)/1#

#=4/1#

Now rewrite.

#4#