Question

multiply.
$3x^{8} \cdot 2y \cdot 8y^{7}x^{5}$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(3\), \(2\), and \(8\). So, \(3\times2\times8 = 48\).

Step2: Multiply the \(x\)-terms

Use the rule \(a^m\cdot a^n=a^{m + n}\) for \(x^8\) and \(x^5\). So, \(x^8\cdot x^5=x^{8 + 5}=x^{13}\).

Step3: Multiply the \(y\)-terms

Use the rule \(a^m\cdot a^n=a^{m + n}\) for \(y\) (which is \(y^1\)) and \(y^7\). So, \(y\cdot y^7=y^{1+7}=y^8\).

Step4: Combine all parts

Combine the coefficient, \(x\)-term, and \(y\)-term. So, the result is \(48x^{13}y^8\).

Answer:

\(48x^{13}y^8\)