Simplifying a fraction with variables..?

Question

http://palcs.digitalschooling.com/brand/media/images/1193/Algebra_2/Chapter_2___lessons_5___8/lesson_5_problem_8.JPG

It's a biggie. (Atleast to me.)

Answer 1

Original equation:
Numerator: 4 c^2 d c^-3 ( 2 c d^-2 )^-2
Denominator: c^0 c^-3 ( c^-2 d )^2

Switch any negative exponents to the other side of the fraction:
Numerator: 4 c^2 d c^3
Denominator: c^0 c^3 ( c^-2 d )^2 ( 2 c d^-2 )^2

Distribute the exponents (where you have parentheses) through:
Numerator: 4 c^2 d c^3
Denominator: c^0 c^3 ( c^-4 d^2 ) ( 2^2 c^2 d^-4 )

Now start grouping exponents on the same bases (you add the exponents)
Numerator: 4 c^5 d
Denominator: c^3 c^-4 d^2 4 c^2 d^-4

Continue:
Numerator: 4 c^5 d
Denominator: c^1 d^-2 4

Now cancel similar bases top and bottom (and the 4):
Numerator: c^4 d^3
Denominator: 1

So the answer is c^4 d^3

Answer 2

The faction as you have shown it can't be made any less complicated. Multiplying suited and backside by skill of 8 can no longer go away you something exciting. one thank you to look at it extremely is to interchange the detrimental sign with a multiplication by skill of -a million. they're comparable. So -(x-y)/8 = -a million * (x-y)/8 you could take up the detrimental sign on the suited or the backside so -(x-y)/8 = (y-x)/8 = (x-y)/(-8) = y/8 - x/8 = -x/8 + y/8 The above words all exhibit an identical selection.

Answer 3

[4 c^2 d c^-3 ( 2 c d^-2 )^-2]/[c^0 c^-3 ( c^-2 d )^2]

Cancel the c^-3 from the numerator and denominator. Replace c^0 with its value, 1.

[4 c^2 d ( 2 c d^-2 )^-2]/[( c^-2 d )^2]

Remove parentheses.

[4c^2d4^-1c^-2d^4]/[c^-4d^2)

Items with negative exponents to other side.

[4c^2dd^4c^4]/[4d^2c^2]

[4 c^6d^5]/[4d^2c^2]

c^4d^3

Just follow the rules that you already know, one step at a time, being careful. :-)