(9x^3y^4)/(16a^4b^2) divided by (45x^4y^2)/(14a^7b)
9x3y4 45x4y2
-------- ÷ --------
16a4b2 14a7b
Invert the second fraction and change
division to multiplication:
9x3y4 14a7b
-------- × --------
16a4b2 45x4y2
Indicate the multiplication of the numerators
and the denominators so that you have just one
fraction:
(9)(14)x3y4a7b
------------------
(16)(45)a4b2x4y2
Begin by simplifying the numbers. Cancel the
9 into the 45, and divide the 14 and the 16
each by 2:
1 7
(9)(14)x3y4a7b
------------------
(16)(45)a4b2x4y2
8 5
So now we have:
7x3y4a7b
------------
40a4b2x4y2
There are no eponentials with like
bases in the numerator or in the
denominator to add the exponents of.
So we subtract exponents of
exponentials with like bases
between numerator and denominator:
We see there is an x3 on top and
an x4 on the bottom. So we subtract
larger minus smaller 4-3 and get 1
and put x1 on the bottom because
the larger exponent, 4, was on the
bottom, and eliminate x from the
top.
7y4a7b
------------
40a4b2x1y2
We see there is a y4 on top and
a y2 on the bottom. So we subtract
larger minus smaller 4-2 and get 2
and put y2 on the top because
the larger exponent, 4, was on the
top, and eliminate y from the
bottom.
7y2a7b
----------
40a4b2x1
We see there is an a7 on top and
an a4 on the bottom. So we subtract
larger minus smaller 7-4 and get 3
and put a3 on the top because
the larger exponent, 7, was on the
top, and eliminate a from the
bottom.
7y2a3b
--------
40b2x1
We give the b on top its understood
exponent of 1
7y2a3b1
---------
40b2x1
We see there is a b1 on top and
a b2 on the bottom. So we subtract
larger minus smaller 2-1 and get 1
and put b1 on the bottom because
the larger exponent, 2, was on the
bottom, and eliminate b from the
top.
7y2a3
--------
40b1x1
We are done except for erasing the
1 exponents, leaving them understood:
7y2a3
-------
40bx
That's the final simplified answer.
Edwin
