Simplify the expression: 2x to the third power times 5x to the eighth power.

To simplify the expression (2x^3 \times 5x^8), you start by multiplying the coefficients and then applying the rules of exponents.

First, multiply the coefficients:

• The coefficients are 2 and 5. When multiplied together, they give you (2 \times 5 = 10).

Next, handle the variables with exponents:

• You have (x^3) and (x^8). When multiplying terms with the same base, you add the exponents. Therefore, (x^3 \times x^8 = x^{3+8} = x^{11}).

Now, combining the results from both parts, you get:

• The simplified expression is (10x^{11}).

Thus, the correct answer to the problem is that the expression simplifies to (10x^{11}). This matches one of the choices provided, confirming it as the correct result.