5/11 Simplify the following expression using the Laws of c^-8d^0cdot c^-3dcdot c^0d (d)/(c^11) (d^2)/(c^8) (d^2)/(c^11)

To simplify the given expression \(c^{-8}d^{0} \cdot c^{-3}d \cdot c^{0}d\), we can use the laws of exponents.<br /><br />First, let's simplify each term individually:<br />- \(c^{-8}\) remains as it is.<br />- \(d^{0}\) is equal to 1, so it can be omitted.<br />- \(c^{-3}\) remains as it is.<br />- \(d\) remains as it is.<br />- \(c^{0}\) is equal to 1, so it can be omitted.<br />- \(d\) remains as it is.<br /><br />Now, let's multiply the terms together:<br />\(c^{-8} \cdot c^{-3} \cdot d \cdot d = c^{-11} \cdot d^{2}\)<br /><br />Therefore, the simplified expression is \(\frac{d^{2}}{c^{11}}\).<br /><br />So, the correct answer is \(\frac{d^{2}}{c^{11}}\).