Question

multiply.
$4w^{5}x^{3} \cdot 2w \cdot 6x^{2}$
simplify your answer as much as possible.
$48w^{6}x^{5}$

Explanation:

Step1: Multiply coefficients

Multiply the numerical coefficients: \(4\times(-2)\times(-6)\).
\(4\times(-2)= -8\), then \(-8\times(-6)=48\).

Step2: Multiply \(w\) terms

For the \(w\) variables, use the exponent rule \(a^m\times a^n = a^{m + n}\). We have \(w^5\times w^1\times w^0\) (the last \(w\) is \(w^1\), and the middle term is \(w^1\)? Wait, original terms: \(4w^5x^3\cdot(-2w)\cdot(-6x^2)\). So \(w\) terms: \(w^5\times w^1\) (since \(-2w = -2w^1\)). So \(w^{5 + 1}=w^6\).

Step3: Multiply \(x\) terms

For \(x\) terms: \(x^3\times x^2\) (since the last term is \(-6x^2\), and the first has \(x^3\), the middle has no \(x\) except in the first term? Wait, original expression: \(4w^5x^3\cdot(-2w)\cdot(-6x^2)\). So \(x\) terms: \(x^3\times x^2=x^{3 + 2}=x^5\).

Step4: Combine all parts

Combine the coefficient, \(w\) term, and \(x\) term: \(48\times w^6\times x^5 = 48w^6x^5\).

Answer:

\(48w^6x^5\)