How do you simplify #(25c^3d^3e^3 - 55c^4d^5e^7 + 35c^8d^7e^6) / (5c^2d^2e^3)#?

Question

How do you simplify #(25c^3d^3e^3 - 55c^4d^5e^7 + 35c^8d^7e^6) /   (5c^2d^2e^3)#?

Nathan Axel · Accepted Answer

#(25c^3d^3e^3−55c^4d^5e^7+35c^8d^7e^6)/(5c^2d^2e^3)# #(25c^3d^3e^3)/(5c^2d^2e^3)  − (55c^4d^5e^7)/(5c^2d^2e^3) +(35c^8d^7e^6)/(5c^2d^2e^3)# #5cd - 11c^2d^3e^4 + 7c^6d^5e^3# If you would like to factor further, the greatest common factor is #cd#: #cd(5-11cd^2e^4 + 7c^5d^4e^3)#

Abigail Allen · Answer

undefined The simplified expression is 5c^3d^3e^3 - 11c^2d^3e^5 + 7c^6d^5e^3.

Avery Alexander · Answer

undefined To simplify $ \frac{25c^3d^3e^3 - 55c^4d^5e^7 + 35c^8d^7e^6}{5c^2d^2e^3} $, you divide each term in the numerator by the denominator. This yields:

$$ \frac{25c^3d^3e^3}{5c^2d^2e^3} - \frac{55c^4d^5e^7}{5c^2d^2e^3} + \frac{35c^8d^7e^6}{5c^2d^2e^3} $$

Then, simplify each term individually:

$$ \frac{25}{5} \cdot \frac{c^{3-2}}{c^{2-2}} \cdot \frac{d^{3-2}}{d^{2-2}} \cdot \frac{e^{3-3}}{e^{3-3}} - \frac{55}{5} \cdot \frac{c^{4-2}}{c^{2-2}} \cdot \frac{d^{5-2}}{d^{2-2}} \cdot \frac{e^{7-3}}{e^{3-3}} + \frac{35}{5} \cdot \frac{c^{8-2}}{c^{2-2}} \cdot \frac{d^{7-2}}{d^{2-2}} \cdot \frac{e^{6-3}}{e^{3-3}} $$

This simplifies to:

$$ 5c \cdot d \cdot 1 - 11c^2 \cdot d^3 \cdot e^4 + 7c^6 \cdot d^5 \cdot e^3 $$

So, the simplified expression is $ 5cd - 11c^2d^3e^4 + 7c^6d^5e^3 $.