Find all the real fourth roots of 256/2401

Answer 1

To find all of the real fourth roots of 256/2401, we first simplify the fraction:

256/2401 = 16/151 = (16/151)^(1/1)

Now, we want to find the fourth root of 16/151:

(16/151)^(1/4) = (16/151)^(1/4)

To simplify, we can rewrite 16 as 2^4:

(2^4/151)^(1/4) = (2^4)^(1/4) / 151^(1/4) = 2 / 151^(1/4)

Therefore, the real fourth roots of 256/2401 are 2/(151)^(1/4) and -2/(151)^(1/4).

Answer 2

wrong

Answer 3

I apologize for the mistake. Let's correct it.

We have the fraction 256/2401, which simplifies to 16/151 when reduced.

To find the real fourth roots of 16/151, we need to calculate (16/151)^(1/4)

Let's first express 16/151 as an exponent:

16/151 = (16/151)^(1/1)

Now, to take the fourth root:

(16/151)^(1/4) = (16/151)^(1/4)

Taking the fourth root can be simplified as follows. Rewrite 16 as 2^4:

(2^4 / 151)^(1/4) = 2^(4/4) / 151^(1/4) = 2 / 151^(1/4)

So, the real fourth roots of 16/151 are 2/(151)^(1/4) and -2/(151)^(1/4).