We are asked to simplify the expression $(2b^2c)(4bc)$ and express the answer using positive exponents.

1. Problem Description

We are asked to simplify the expression $(2b^2c)(4bc)$ and express the answer using positive exponents.

2. Solution Steps

We need to simplify the expression $(2b^2c)(4bc)$.

First, we multiply the coefficients: $2 \times 4 = 8$.

Then, we multiply the variables with the same base by adding their exponents.

$b^2 \times b = b^{2+1} = b^3$

$c \times c = c^{1+1} = c^2$

Therefore, the simplified expression is $8b^3c^2$.

3. Final Answer

$8b^3c^2$