Question

multiply.
$4u^{8}x^{8}\cdot 2x^{2}\cdot 5u$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(4\), \(2\), and \(5\). So, \(4\times2\times5 = 40\).

Step2: Multiply the \(u\)-terms

For the \(u\)-terms, we have \(u^{8}\) and \(u\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(u^{8}\cdot u=u^{8 + 1}=u^{9}\).

Step3: Multiply the \(x\)-terms

For the \(x\)-terms, we have \(x^{8}\) and \(x^{2}\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(x^{8}\cdot x^{2}=x^{8+2}=x^{10}\).

Step4: Combine all the terms

Now, combine the coefficient, the \(u\)-term, and the \(x\)-term. We get \(40u^{9}x^{10}\).

Answer:

\(40u^{9}x^{10}\)