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2. \( x^{3} \cdot\left(-3 x^{4}\right) x^{-2} \)

Ask by Collins Lewis. in South Africa
Jan 16,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The simplified expression is \( -3x^{5} \).

Solution

To simplify the expression: \[ x^{3} \cdot\left(-3 x^{4}\right) \cdot x^{-2} \] **Step 1: Multiply the coefficients.** The coefficients are \(1\), \(-3\), and \(1\): \[ 1 \times (-3) \times 1 = -3 \] **Step 2: Add the exponents of \(x\).** Using the rule \(x^a \cdot x^b = x^{a+b}\): \[ x^{3} \cdot x^{4} \cdot x^{-2} = x^{3+4-2} = x^{5} \] **Combine the results:** \[ -3x^{5} \] **Final Answer:** \[ -3x^{5} \]

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Simplify this solution

Beyond the Answer

Let's simplify the expression step by step! First, we'll combine the bases of \(x\): \[ x^3 \cdot (-3x^4) \cdot x^{-2} = -3 \cdot (x^{3 + 4 - 2}) = -3x^{5} \] So, the simplified result is \( -3x^5 \). Now that you have a cleaned-up expression, it's always a good idea to double-check your work. You could use the properties of exponents and break it down into parts if needed or even plot the function for a visual understanding!

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