Simplify the expression $(14fg^2h^2)(3f^4g^2h^2)$.

1. Problem Description

Simplify the expression $(14fg^2h^2)(3f^4g^2h^2)$.

2. Solution Steps

To simplify the expression $(14fg^2h^2)(3f^4g^2h^2)$, we will multiply the coefficients and combine like terms using the rule $x^a \cdot x^b = x^{a+b}$.

First, multiply the coefficients:

$14 \cdot 3 = 42$

Next, multiply the $f$ terms:

$f \cdot f^4 = f^{1+4} = f^5$

Then, multiply the $g$ terms:

$g^2 \cdot g^2 = g^{2+2} = g^4$

Finally, multiply the $h$ terms:

$h^2 \cdot h^2 = h^{2+2} = h^4$

Combine all the results:

$42 f^5 g^4 h^4$

3. Final Answer

The simplified expression is $42f^5g^4h^4$.