Question

Detemine o valor de ±⁴√256

Answer 1

Lembrete:

๏ $\sqrt[c]{a^b}=a^{\frac{b}{c}}$
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Fatorando o numero 256:

256 | 2
128 | 2
64   | 2
32   | 2
16   | 2
8     | 2
4     | 2
2     | 2
1                 $256\:=\:2^8=4^4$
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$x=\pm \sqrt[4]{256}\\x=\pm \sqrt[4]{4^4}\\x=\pm 4^{\frac{4}{4}}\\\boxed{\bold{x=\pm 4}}$