d: ((3^-4 cdot 3))/(3^-8) cdot 3^5

To simplify the expression \( d: \frac{\left(3^{-4} \cdot 3\right)}{3^{-8}} \cdot 3^{5} \), we can follow these steps:<br /><br />1. Simplify the numerator: \( 3^{-4} \cdot 3 = 3^{-4+1} = 3^{-3} \)<br />2. Simplify the denominator: \( 3^{-8} \)<br />3. Divide the numerator by the denominator: \( \frac{3^{-3}}{3^{-8}} = 3^{-3 - (-8)} = 3^{5} \)<br />4. Multiply the result by \( 3^{5} \): \( 3^{5} \cdot 3^{5} = 3^{5+5} = 3^{10} \)<br /><br />Therefore, the simplified expression is \( d = 3^{10} \).