Question

multiply.
$2u^{7}x^{4} \cdot 6x^{6} \cdot 4u$
simplify your answer as much as possible.

Explanation:

Step1: Multiply coefficients

Multiply the numerical coefficients: \(2 \times 6 \times 4 = 48\)

Step2: Combine like terms for \(u\)

For the variable \(u\), use the rule \(a^m \cdot a^n = a^{m + n}\). So \(u^7 \cdot u = u^{7 + 1}=u^8\)

Step3: Combine like terms for \(x\)

For the variable \(x\), use the same rule: \(x^4 \cdot x^6 = x^{4 + 6}=x^{10}\)

Step4: Combine all parts

Multiply the coefficient, \(u\)-term, and \(x\)-term together: \(48u^8x^{10}\)

Answer:

\(48u^{8}x^{10}\)