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:

$\sqrt[4]{256} = 256^{\frac{1}{4}}$

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

$\sqrt[4]{256} = 256^{\frac{1}{4}} = (2^8)^{\frac{1}{4}} = 2^{\frac{8}{4}} = 2^2 = 4$