Question

which is equivalent to \\(\frac{10a^{2}b^{3}c^{4}+20a^{3}b^{2}c^{2}+25a^{2}b^{4}c^{3}}{5abc}\\)?

a. \\(2ab^{2}c^{3} + 4a^{2}bc + 5ab^{3}c^{2}\\)

b. \\(2ab^{2}c^{3} + 20a^{3}\\)

c. \\(10a^{2}b^{3}c^{4}\\)

d. \\(10a^{2}b^{3}c^{4} + 20a^{3}b^{2}c^{2} + 5ab^{3}c^{2}\\)

e. \\(1,000a^{6}b^{8}c^{8}\\)

Explanation:

Step1: Divide each term by 5abc

For the first term: $\frac{10a^{2}b^{3}c^{4}}{5abc}=\frac{10}{5}a^{2 - 1}b^{3 - 1}c^{4 - 1}=2ab^{2}c^{3}$
For the second term: $\frac{20a^{3}b^{2}c^{2}}{5abc}=\frac{20}{5}a^{3 - 1}b^{2 - 1}c^{2 - 1}=4a^{2}bc$
For the third term: $\frac{25a^{2}b^{4}c^{3}}{5abc}=\frac{25}{5}a^{2 - 1}b^{4 - 1}c^{3 - 1}=5ab^{3}c^{2}$

Step2: Combine the results

The expression simplifies to $2ab^{2}c^{3}+4a^{2}bc + 5ab^{3}c^{2}$

Answer:

A. $2ab^{2}c^{3}+4a^{2}bc + 5ab^{3}c^{2}$