Question

multiply.
$2x\cdot 3x^{6}v^{2}\cdot 8v^{6}$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(2 \times 3 \times 8 = 48\)

Step2: Multiply the \(x\)-terms

For the \(x\)-terms, use the rule \(a^m \cdot a^n = a^{m + n}\). Here, \(x \cdot x^6 = x^{1 + 6}=x^7\)

Step3: Multiply the \(v\)-terms

For the \(v\)-terms, use the same exponent rule: \(v^2 \cdot v^6 = v^{2 + 6}=v^8\)

Step4: Combine all parts

Combine the coefficient, \(x\)-term, and \(v\)-term: \(48x^7v^8\)

Answer:

\(48x^{7}v^{8}\)