Simplify, explain this to me please.?

Question

-4x^3y^2 * -4xy^3
_________ _________
2x^2y^3 10xy^2

Answer 1

-4x^3y^2. . . . -4xy^3
_________ x _________ =
2x^2y^3. . . . . 10xy^2

Start cancelling like terms, leaving
-2x(-2)y
---------- =
y(5)

4x/5

Answer 2

I see from the page's source code that you meant to write two different fractions multiplied by each other:

(-4(x^3)(y^2) / 2(x^2)(y^3) ) * ( -4x(y^3) / 10x(y^2) )

You can multiply the top and bottom of a fraction with the same non-zero number and the fraction will remain the same (this is because it's the equivalent of multiplying by n/n, which is always equal to one). Some other handy rules to keep in mind are these:

n^(-p) = 1 / n^(p)
1 / n^(-p) = n^p
n^p / n^q = n^(p-q)
n^p / n^q = 1 / n^(q-p)

Taking the first fraction: (-4(x^3)(y^2) / 2(x^2)(y^3))
You can divide the top and bottom by 2 and get:
(-2(x^3)(y^2) / (x^2)(y^3))

Also, having x^3 on top and x^2 on the bottom means having x^(3-2) = x^1 = x on top:

(-2x(y^2) / (y^3))

Similarly, having y^2 on top and y^3 on the bottom means you can have y^(3-2) = y on the bottom. This gives you: -2x / y

Do the same techniques for the second fraction and you get
-2y / 5.

When these two fractions are multiplied together, you get (-2x * -2y) / (5y), or 4xy / 5y. The ys cancel to leave 4x / 5

Answer 3

-4x^3y^2 * -4xy^3
_________ _________
2x^2y^3 10xy^2



is this what you mean

(-4x^3y^2)/(2x^2y^3) * (-4xy^3)/(10xy^2)

(-4x^3y^2)/(2x^2y^3) = (-2x/y) First term Simplified

(-4xy^3)/(10xy^2) = (-2xy/5) Second term Simplified


(-2x/y)*(-2xy/5) = (4xy*x)/(5y) Multiply together



To multiply fractions:

1). Simplify the fractions if not in lowest terms.
2). Multiply the numerators of the fractions to get the new numerator.
3). Multiply the denominators of the fractions to get the new denominator.

EXAMPLE

1/5 x 2/3 = (1x2)/(5x3) = 2/15 Thats what we did above
http://www.math.com/school/subject1/lessons/S1U4L4GL.html#sm1

(-2x/y)*(-2xy/5) = (4xy*x)/(5y) Multiply together

(-2x*-2xy)/(y*5) = (4xy*x)/(5y)

Answer 4

never took that.