Eghth grade C. 18 Multiply and divide powers: variable bases 85 P \[ \begin{array}{l}\text { ()) Simplify. Express your answer using positive exponents. } \\ \qquad\left(10 u^{5}\right)\left(5 u^{7}\right)\left(8 u^{4}\right)\end{array} \]

To simplify the expression \((10 u^{5})(5 u^{7})(8 u^{4})\), first multiply the coefficients: \(10 \times 5 \times 8 = 400\). Next, combine the powers of \(u\) by adding their exponents: \(u^{5} \times u^{7} \times u^{4} = u^{(5 + 7 + 4)} = u^{16}\). So, the final simplified expression is \(400 u^{16}\). Remember to always combine coefficients and add the exponents when working with powers of the same base. It's a fun practice to write down each step, as it solidifies your understanding of how to manipulate exponents. This foundation will help you tackle more complex algebraic expressions down the road!