Answer:
n=4
Step-by-step explanation:
[tex]\sqrt[n]{256} =8^{\frac{1}{3} } *8^{\frac{1}{3} } \\256^{\frac{1}{n} } =(2^{3} )^{\frac{1}{3} } *(2^{3} )^{\frac{1}{3} } \\(2^{8})^{\frac{1}{n} } =2^{3 \times \frac{1}{3} } *2^{3 \times \frac{1}{3} } \\2^{\frac{8}{n} } =2 \times 2\\2^{\frac{8}{n} } =2^{2} \\\frac{8}{n} =2\\n=\frac{8}{2} =4[/tex]
