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

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

• A. 10x to the eighth power
• B. 10x to the eleventh power
• C. 7x to the eleventh power
• D. 12x to the ninth power

Answer: (B)

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.

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.