Which expression is equivalent to (64y^100)^(1)/(2) 8y^10 8y^50 32y^10 32y^50

To find the equivalent expression for \((64y^{100})^{\frac{1}{2}}\), we can use the properties of exponents.<br /><br />First, let's break down the expression inside the parentheses:<br />\[<br />(64y^{100})^{\frac{1}{2}}<br />\]<br /><br />We can separate the constant and the variable parts:<br />\[<br />64^{\frac{1}{2}} \cdot (y^{100})^{\frac{1}{2}}<br />\]<br /><br />Now, let's evaluate each part separately:<br /><br />1. Evaluate \(64^{\frac{1}{2}}\):<br />\[<br />64^{\frac{1}{2}} = \sqrt{64} = 8<br />\]<br /><br />2. Evaluate \((y^{100})^{\frac{1}{2}}\):<br />\[<br />(y^{100})^{\frac{1}{2}} = y^{100 \cdot \frac{1}{2}} = y^{50}<br />\]<br /><br />Combining these results, we get:<br />\[<br />8 \cdot y^{50} = 8y^{50}<br />\]<br /><br />Therefore, the expression equivalent to \((64y^{100})^{\frac{1}{2}}\) is:<br />\[<br />8y^{50}<br />\]<br /><br />So, the correct answer is:<br />\[<br />8y^{50}<br />\]