Question

multiply.
$2u^6 \cdot 7v^4 u^8 \cdot 2v$
simplify your answer as much as possible.

Explanation:

Step1: Group coefficients and like variables

Group the numerical coefficients (2, 7, 2) together and the \(u\)-terms (\(u^6\), \(u^8\)) and \(v\)-terms (\(v^4\), \(v\)) together. So we have \((2\times7\times2)\times(u^6\times u^8)\times(v^4\times v)\).

Step2: Multiply the coefficients

Calculate the product of the coefficients: \(2\times7\times2 = 28\).

Step3: Multiply the \(u\)-terms using exponent rule

For multiplying variables with exponents, use the rule \(a^m\times a^n=a^{m + n}\). For \(u^6\times u^8\), we get \(u^{6 + 8}=u^{14}\).

Step4: Multiply the \(v\)-terms using exponent rule

For \(v^4\times v\) (note that \(v = v^1\)), we use the same exponent rule: \(v^{4+1}=v^5\).

Step5: Combine the results

Multiply the results from Step2, Step3, and Step4 together: \(28\times u^{14}\times v^5 = 28u^{14}v^5\).

Answer:

\(28u^{14}v^5\)