((4)/(7))^3 cdot(1 cdot 75)^2

To solve the expression \( \left(\frac{4}{7}\right)^{3} \cdot(1 \cdot 75)^{2} \), we need to evaluate each part separately and then multiply the results.<br /><br />First, let's evaluate \( \left(\frac{4}{7}\right)^{3} \):<br /><br />\[ \left(\frac{4}{7}\right)^{3} = \frac{4^3}{7^3} = \frac{64}{343} \]<br /><br />Next, let's evaluate \( (1 \cdot 75)^{2} \):<br /><br />\[ (1 \cdot 75)^{2} = 75^2 = 5625 \]<br /><br />Now, we multiply the two results together:<br /><br />\[ \left(\frac{64}{343}\right) \cdot 5625 = \frac{64 \cdot 5625}{343} \]<br /><br />To simplify this, we can multiply the numerator:<br /><br />\[ 64 \cdot 5625 = 358400 \]<br /><br />So, the expression becomes:<br /><br />\[ \frac{358400}{343} \]<br /><br />To simplify this fraction, we can divide the numerator by the denominator:<br /><br />\[ \frac{358400}{343} \approx 1048.21 \]<br /><br />Therefore, the value of the expression \( \left(\frac{4}{7}\right)^{3} \cdot(1 \cdot 75)^{2} \) is approximately 1048.21.