math destroyer test 4 question 10 and 13??

[demolitionlvr]

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10. simplify

(a^8b^2c^5)/^3 sqrt( a^6b^9c^12)

Math Destroyer's Explanation:
(a^8b^2c^5)/^3 sqrt( a^6b^9c^12) = (a^8b^2c^5)/(a^2b^3c^4) = answer is (a^6c)/b

My question: I don't understand the bold part of the expression...I have never seen that before and how does that translate to the first part of the simplification??

13. Given that there are 231 cubic inches in 1 gallon, which expression represents the number of gallons in two cubic yards?

Math Destroyer's Explanation:
Two cubic yards contain 2 (36)(36)(36) cubic inches. Dividing this by 231 and rearranging, we get (2x6^6)/ 231.

My question: Why do you multiple 36 three times? I thought it was sufficient to just multiply 2 by 12inches and 3 feet..

 

[KyoPhan]

I think #10 is just poorly typed out. This is how it should look like, and you probably seen this.

For #13, the way I do it is that I try to make sure that the units cancels each other out. If you keep the labels correct and conversions, you should get the right answer.

 

[demolitionlvr]

Thank you very much for taking the time to thoroughly answer this! Appreciate it! 🙂