The expression that is equivalent to [tex](256 x^{16})^{\frac{1}{4} }[/tex] is [tex]4x^4[/tex].
The given parameters:
The given expression can be simplified by applying laws of indicial expressions as follows;
[tex](256 x^{16})^{\frac{1}{4} } = (2^8 x^{16})^{\frac{1}{4} } \\\\[/tex]
The expression can be simplified further as follows;
[tex](2^8 x^{16})^{\frac{1}{4} } = (2^8)^{\frac{1}{4} } \times (x^{16}) ^{\frac{1}{4} } = (2^2) \times (x ^4) = 4x^4\\\\[/tex]
Thus, the expression that is equivalent to [tex](256 x^{16})^{\frac{1}{4} }[/tex] is [tex]4x^4[/tex].
Learn more about laws of indices here: https://brainly.com/question/170984
