Select all the expressions that are equivalent to (4^-1)^7 (1)/(4^-7) 4^-7 (1)/(4^7) 4^6 A. B B, C A. B, C ) D

To determine which expressions are equivalent to \((4^{-1})^{7}\), we need to simplify this expression first.<br /><br />\[<br />(4^{-1})^{7} = 4^{-1 \cdot 7} = 4^{-7}<br />\]<br /><br />Now, let's evaluate each given option:<br /><br />1. \(\frac{1}{4^{-7}}\)<br /><br /> Simplifying this expression:<br /> \[<br /> \frac{1}{4^{-7}} = 4^{7}<br /> \]<br /> This is not equivalent to \(4^{-72. \(4^{-7}\)<br /><br /> This is already in the simplified form and is equivalent to \(4^{-7}\).<br /><br />3. \(\frac{1}{4^{7}}\)<br /><br /> Simplifying this expression:<br /> \[<br /> \frac{1}{4^{7}} = 4^{-7}<br /> \]<br /> This is equivalent to \(4^{-7}\).<br /><br />4. \(4^{6}\)<br /><br /> This is not equivalent to \(4^{-7}\).<br /><br />So, the expressions that are equivalent to \((4^{-1})^{7}\) are:<br /><br />- \(4^{-7}\)<br />- \(\frac{1}{4^{7}}\)<br /><br />Therefore, the correct answer is:<br /><br />B. C