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Find the root. Assume that the variable represents a nonnegative real number

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2 Answers

Hi Theresa,
So to find the root, we have to remember the Laws of Exponents for this problem.
1st, we can separate the radicand (everything under the root sign) as two different bases: 625*x20. So the problem now looks like 4√625 * 4√x20
2nd, because of the Laws of Exponents, we know that the 4√ of x is just x1/4. So we can change 4√625 * 4√x20 to (625)1/4 * (x20)1/4.
3rd, now we can simplify the problem, again using the Law of Exponents. (625)1/4=5 and (x20)1/4=x20/4. So the entire problem looks like 5*x20/4, which equals 5x5.
So your answer is 5x5 
Hope this helps and makes sense too.
Best regards,
Micheal C.
simplify fourth root of (625 * x^20)    
this can be written as (fourth root of 625)(fourth root of x^20)
fourth root of 625 can be written (625)^(1/4)
this means solve n^4=625
therefore n=5
the fourth root of (x^20) can be written as (x^20)^(1/4)=x^5
answer: 5(x^5)