Question

multiply.
$2x^{6}w^{4} \cdot 6x \cdot 4w^{6}$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(2\), \(6\), and \(4\). So, \(2\times6\times4 = 48\).

Step2: Multiply the \(x\)-terms

For the \(x\)-terms, we have \(x^{6}\) and \(x\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(x^{6}\cdot x=x^{6 + 1}=x^{7}\).

Step3: Multiply the \(w\)-terms

For the \(w\)-terms, we have \(w^{4}\) and \(w^{6}\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), we get \(w^{4}\cdot w^{6}=w^{4+6}=w^{10}\).

Step4: Combine all the terms

Combine the results from Step 1, Step 2, and Step 3. So, the product is \(48\times x^{7}\times w^{10}=48x^{7}w^{10}\).

Answer:

\(48x^{7}w^{10}\)