SOLUTION: What would you do to simplify the 3rd root of 125^n*5^(4n)/25^-n without negative exponents and decimals in the final answer?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: What would you do to simplify the 3rd root of 125^n*5^(4n)/25^-n without negative exponents and decimals in the final answer?      Log On


   

Question 147841: What would you do to simplify the 3rd root of 125^n*5^(4n)/25^-n without negative exponents and decimals in the final answer?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Remember exponentiation rules.
x%5EM%2Ax%5EN=x%5E%28M%2BN%29
%28x%5EM%29%5EN=X%5E%28M%2AN%29
Let's look at the individual terms first and make some simplifications.
125 and 25 are both divisible by 5.
Put them into lowest terms of base 5.
125%5En=%285%5E3%29%5En
125%5En=5%5E%283n%29
.
.
.
25%5E%28-n%29=%285%5E2%29%5E%28-n%29
25%5E%28-n%29=5%5E%28-2n%29
25%5E%28-n%29=1%2F%285%5E%282n%29%29
1%2F%2825%5E%28-n%29%29=%285%5E%282n%29%29
.
.
.
Now let's put it all together.


%28%28%28125%5En%29%285%5E%284n%29%29%29%2F%2825%5E%28-n%29%29%29%5E%281%2F3%29=5%5E%283n%29