Respuesta :

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

[tex] 256 = 2^8 [/tex]

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

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

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

[tex] (a^b)^c = a^{bc} [/tex]

Put together everything we said so far to write

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


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