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

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

4√625x^20

### 2 Answers by Expert Tutors

Micheal C. | Flexible and Young Math and English TutorFlexible and Young Math and English Tuto...
4.9 4.9 (103 lesson ratings) (103)
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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.

Hope this helps and makes sense too.

Best regards,
Micheal C.

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (7 lesson ratings) (7)
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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
625=25*25=5*5*5*5
therefore n=5
the fourth root of (x^20) can be written as (x^20)^(1/4)=x^5