The problem is to simplify the expression $(2x^3)(c^2)(-10c^3)(x^7)$.

1. Problem Description

The problem is to simplify the expression $(2x^3)(c^2)(-10c^3)(x^7)$.

2. Solution Steps

We are given the expression $(2x^3)(c^2)(-10c^3)(x^7)$.

We will rearrange the terms and group like terms together:

$2 \cdot (-10) \cdot x^3 \cdot x^7 \cdot c^2 \cdot c^3$

Now, we multiply the coefficients and use the property $x^a \cdot x^b = x^{a+b}$ to simplify the powers of $x$ and $c$.

$2 \cdot (-10) = -20$

$x^3 \cdot x^7 = x^{3+7} = x^{10}$

$c^2 \cdot c^3 = c^{2+3} = c^5$

Therefore, the simplified expression is:

$-20x^{10}c^5$

3. Final Answer

The final answer is $-20x^{10}c^5$.