Question

How do you simplify `((-22y^4)/(21xz^2))``((10x^9) / (-4y^7z^3))``((-7yz^5)/(11x^3))`?

Answer 1

=`(-5x^5)/(3y^2)`

Explanation:

This is plain multiplication of algebraic fractions:

1. Determine the overall sign: even number of negatives `rArr` pos

2. Cancel the numbers wherever possible.

3. Collect all the variables together in numerator and denominator.
4. Simplify

`(-22y^4 xx 10x^9 xx -7yz^5)/(21xz^2 xx -4y^7z^3 xx 11x^3)`

`= (-cancel22^2y^4 xx cancel 10^5x^9 xx cancel7yz^5)/(cancel21^3xz^2 xx cancel4^2y^7z^3 xx cancel11x^3)`

=`(-cancel2y^4 xx 5x^9 xx yz^5)/(3xz^2 xx cancel2y^7z^5 xx x^3)` = `(-5x^9y^5z^5)/(3x^4y^7z^5)`

=`(-5x^5)/(3y^2)`

Answer 2

Just a very slightly different approach (basically the same thing)

`" "-(5x^5)/(3y^5)`

Explanation:

`("Product of numerator"->"positive")/("product of denominator"->"negative") ->"negative"`

Giving:`" "(-1)xx (22xx10xx7xxy^4x^9yz^5 )/(21xx4xx11xx xz^2y^7z^3x^3)`

`" "(-1)xx(1540)/942xx(x^9y^5z^5 )/( x^4y^7z^5)`

`" "(-1)xx5/3xxx^5/y^2`

`" "-(5x^5)/(3y^5)`