Question

Find the indicator real nth root

Answer 1

It can be useful to know the prime factorization of the number:

`256 = 2^8`

Then, remember that the n-th root of a number is the same as that number to the 1/n-th power:

`\sqrt[4]{256} = 256^{(1)/(4)}`

Finally, you have to remember the rule for raising a power to another power, i.e. you multiply the exponents:

`(a^b)^c = a^(bc)`

Put together everything we said so far to write

`\sqrt[4]{256} = 256^{(1)/(4)} = (2^8)^{(1)/(4)} = 2^{(8)/(4)} = 2^2 = 4`