Question

multiply.
$5v^{4} \cdot 2y^{4}v^{2} \cdot 4y$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(5\), \(2\), and \(4\).
\(5\times2\times4 = 40\)

Step2: Multiply the \(v\)-terms

For the \(v\)-terms \(v^{4}\) and \(v^{2}\), use the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\).
\(v^{4}\cdot v^{2}=v^{4 + 2}=v^{6}\)

Step3: Multiply the \(y\)-terms

For the \(y\)-terms \(y^{4}\) and \(y\), use the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\).
\(y^{4}\cdot y=y^{4+1}=y^{5}\)

Step4: Combine all the parts

Combine the coefficient, \(v\)-term, and \(y\)-term together.
\(40\times v^{6}\times y^{5}=40v^{6}y^{5}\)

Answer:

\(40v^{6}y^{5}\)