SOLUTION: Can someone please explain to me how 32^(4/5) equals 16. This is dealing with rational exponents and I am not sure nor can I figure it out how they came up with 16.
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Question 190884This question is from textbook
: Can someone please explain to me how 32^(4/5) equals 16. This is dealing with rational exponents and I am not sure nor can I figure it out how they came up with 16.
What are the steps to come up with this answer?
ANy help at all would be greatly appreciated.
This question is from textbook
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
^{\frac{4}{5}})
... Start with the given expression
Convert to radical notation
Note: ^{\frac{m}{n}}=\sqrt[n]{x^m})
and ^{\frac{m}{n}}=\left(\sqrt[n]{x}\right)^{m})
. I'm using the second identity.
Take the 5th root of 32 to get 2. Remember, since , this means that
Raise 2 to the 4th power to get 16
So ^{\frac{4}{5}}=16)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the rule:
^n)
So:
^4)
Now you can either start punching buttons on your calculator, or just realize that 
and 
to be able to write:
^4 = 2^4 = 16)
John
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