Question

multiply.
\\( 2v^9 \cdot 7w^3v^6 \cdot 2w \\)
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

First, multiply the numerical coefficients together. The coefficients are 2, -7, and -2. So, \(2\times(-7)\times(-2)\). When multiplying two negative numbers, the result is positive, so \((-7)\times(-2) = 14\), then \(2\times14 = 28\).

Step2: Multiply the \(v\)-terms

For the variables with base \(v\), we have \(v^{9}\) and \(v^{6}\). Using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\), so \(v^{9}\cdot v^{6}=v^{9 + 6}=v^{15}\).

Step3: Multiply the \(w\)-terms

For the variables with base \(w\), we have \(w^{3}\) and \(w\) (which is \(w^{1}\)). Using the exponent rule again, \(w^{3}\cdot w^{1}=w^{3+1}=w^{4}\).

Step4: Combine all parts

Now, combine the coefficient and the multiplied variable terms. So we get \(28v^{15}w^{4}\).

Answer:

\(28v^{15}w^{4}\)