SOLUTION: Simplify -(8a^3/27)-4/3 (this is an exponent-4/3)(so is the three)This problem isnt' in a book! please help!

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Question 180130: Simplify -(8a^3/27)-4/3 (this is an exponent-4/3)(so is the three)This problem isnt' in a book! please help!
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-%28%288a%5E3%29%2F%2827%29%29%5E%28-4%2F3%29 Start with the given expression


-%2827%2F%288a%5E3%29%29%5E%284%2F3%29 Flip the fraction to make the exponent positive


Note: %28a%2Fb%29%5E%28-2%29=%28b%2Fa%29%5E2



-%28root%283%2C27%2F%288a%5E3%29%29%29%5E4 Convert to radical notation


-%28root%283%2C27%29%2Froot%283%2C8a%5E3%29%29%5E4 Break up the root.


-%283%2Froot%283%2C8a%5E3%29%29%5E4 Take the cube root of 27 to get 3


-%283%2F%282a%29%29%5E4 Take the cube root of 8a%5E3 to get 2a. Note: %282a%29%5E3=2%5E3%2Aa%5E3=8a%5E3


-3%5E4%2F%282a%29%5E4 Distribute the outer exponent


-81%2F%282a%29%5E4 Raise 3 to the 4th power to get 81


-81%2F%2816a%5E4%29 Raise 2a to the 4th power to get 16a%5E4


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Answer:


So -%28%288a%5E3%29%2F%2827%29%29%5E%28-4%2F3%29=-81%2F%2816a%5E4%29 where a%3E0

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+-%28%288a%5E3%29%2F27%29%5E%28-%284%2F3%29%29 (I hope this is right)
I note that 27+=+3%5E3
and 8+=+2%5E3
+-%28%28%282a%2F3%29%5E3%29%5E%28-%284%2F3%29%29%29
-%28%282a%2F3%29%5E%28-4%29%29
-%283%2F%282a%29%29%5E4 answer
check: suppose a+=+3
-%283%2F%282%2A3%29%29%5E4
-%281%2F2%29%5E4
and
+-%28%288a%5E3%29%2F27%29%5E%28-%284%2F3%29%29%29
+-%288%5E%28-%284%2F3%29%29%29
+-%281+%2F%288%5E%284%2F3%29%29%29
-%281%2F%282%5E4%29%29
-%281%2F2%29%5E4
OK