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

^{4}√625x^20

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

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Fullerton, CA

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*x^{20}. So the problem now looks like ^{4}√625 * ^{4}√x^{20}

2nd, because of the Laws of Exponents, we know that the 4√ of x is just x^{1/4}. So we can change ^{4}√625 *
^{4}√x^{20} to (625)^{1/4} * (x^{20})^{1/4}.

3rd, now we can simplify the problem, again using the Law of Exponents. (625)^{1/4}=5 and (x^{20})^{1/4}=x^{20/4}. So the entire problem looks like 5*x^{20/4}, which equals 5x^{5}.

So your answer is **5x**^{5}^{ }

Hope this helps and makes sense too.

Best regards,

Micheal C.

Saugus, MA

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

answer: 5(x^5)

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