Question

multiply.
$3u^9 w^9 \cdot 4w^9 \cdot 3u$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(3\), \(4\), and \(3\). So, \(3\times4\times3 = 36\).

Step2: Multiply the \(u\)-terms

For the \(u\)-terms, we have \(u^{9}\) and \(u\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(u^{9}\cdot u=u^{9 + 1}=u^{10}\).

Step3: Multiply the \(w\)-terms

For the \(w\)-terms, we have \(w^{9}\) and \(w^{9}\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(w^{9}\cdot w^{9}=w^{9+9}=w^{18}\).

Step4: Combine the results

Combine the coefficient, \(u\)-term, and \(w\)-term together. So the result is \(36u^{10}w^{18}\).

Answer:

\(36u^{10}w^{18}\)