Question

multiply.
$2x^2 \cdot 2u \cdot 7u^4 x^3$
simplify your answer as much as possible.

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(2\times2\times7 = 28\)

Step2: Combine like variables for \(x\)

For the \(x\) terms, use the rule \(a^m\cdot a^n=a^{m + n}\). So \(x^{2}\cdot x^{3}=x^{2 + 3}=x^{5}\)

Step3: Combine like variables for \(u\)

For the \(u\) terms, use the same exponent rule. \(u\cdot u^{4}=u^{1+4}=u^{5}\)

Step4: Combine all results

Multiply the coefficient result with the combined \(x\) and \(u\) results: \(28\times x^{5}\times u^{5}=28x^{5}u^{5}\)

Answer:

\(28x^{5}u^{5}\)