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

Question

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

 

⁴√625x^20

Answer 1

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 x^1/4. 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=x^20/4. So the entire problem looks like 5*x^20/4, which equals 5x⁵.

 

So your answer is 5x⁵ 

 

Hope this helps and makes sense too.

 

Best regards,

Micheal C.

 

Answer 2

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)