Question

multiply.
$2x^{5}w^{9} \cdot 2x \cdot 5w^{9}$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(2\times2\times5 = 20\)

Step2: Multiply the \(x\)-terms

For the \(x\)-terms, use the rule \(a^m\cdot a^n=a^{m + n}\). So \(x^5\cdot x=x^{5 + 1}=x^6\)

Step3: Multiply the \(w\)-terms

For the \(w\)-terms, use the rule \(a^m\cdot a^n=a^{m + n}\). So \(w^9\cdot w^9=w^{9+9}=w^{18}\)

Step4: Combine the results

Combine the coefficient, \(x\)-term, and \(w\)-term: \(20x^6w^{18}\)

Answer:

\(20x^{6}w^{18}\)