Question

multiply.
4y cdot 5w^{5} cdot 2y^{3}w^{5}
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(4 \times 5 \times 2 = 40\)

Step2: Multiply the \(y\)-terms

For the \(y\)-terms, use the rule \(a^m \cdot a^n = a^{m + n}\). Here, \(y^1 \cdot y^3 = y^{1 + 3}=y^4\)

Step3: Multiply the \(w\)-terms

For the \(w\)-terms, use the same exponent rule: \(w^5 \cdot w^5 = w^{5 + 5}=w^{10}\)

Step4: Combine the results

Combine the coefficient, \(y\)-term, and \(w\)-term: \(40y^4w^{10}\)

Answer:

\(40y^4w^{10}\)