Questions: Use the product rule to simplify. [ (-2 x^3)(2 x^8) ]

Transcript text: Use the product rule to simplify. \[ \left(-2 x^{3}\right)\left(2 x^{8}\right) \]

Solution

Solution Steps

To simplify the expression using the product rule, multiply the coefficients and add the exponents of the like bases. The product rule for exponents states that \(a^m \cdot a^n = a^{m+n}\).

Step 1: Identify the Expression

We start with the expression \( \left(-2 x^{3}\right)\left(2 x^{8}\right) \).

Step 2: Multiply the Coefficients

The coefficients are \(-2\) and \(2\). Multiplying these gives: \[ -2 \cdot 2 = -4 \]

Step 3: Add the Exponents

The exponents are \(3\) and \(8\). Adding these gives: \[ 3 + 8 = 11 \]

Step 4: Combine the Results

Combining the results from the previous steps, we have: \[ -4 x^{11} \]

Final Answer

\(\boxed{-4 x^{11}}\)

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