How do you simplify #( 4x^2) /( 5y^2) * ( 15xy) /( 24x^2 y^2) #?

Question

Isaiah Anthony · Accepted Answer

#x/(2y^3)#

You can simplify this expression by cancelling like terms that can be found in the numerator and denominator of the two fractions that are being multiplied.

Your starting expression looks like this

#(4x^2)/(5y^2) * (15xy)/(24x^2y^2)#

You can emphasize the terms that can be cancelled by rewriting the expression as

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

The simplified expression will thus be

#(color(red)(cancel(color(black)(4x^2))))/(color(orange)(cancel(color(black)(5))) * y^2) * (color(orange)(cancel(color(black)(5))) * 3 * x * color(purple)(cancel(color(black)(y))))/(color(red)(cancel(color(black)(4x^2))) * 6 * color(purple)(cancel(color(black)(y))) * y) = (3x)/(6y^3) = color(green)(x/(2y^3)#

Eli Assouline · Answer

undefined To simplify the expression (4x^2) / (5y^2) * (15xy) / (24x^2 y^2), we can combine the fractions by multiplying the numerators and denominators together.

First, let's multiply the numerators: 
(4x^2) * (15xy) = 60x^3y

Next, let's multiply the denominators: 
(5y^2) * (24x^2 y^2) = 120x^2 y^4

Now, we can simplify the expression by dividing the numerator by the denominator: 
(60x^3y) / (120x^2 y^4) = 1/2x^(3-2)y^(1-4) = 1/2xy^(-3)

Therefore, the simplified expression is 1/2xy^(-3).