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To simplify the expression \(\frac{(x^4 \cdot x^{11})^3}{x^2}\), we can follow these steps: 1. **Combine the exponents in the numerator**: \[ x^4 \cdot x^{11} = x^{4 + 11} = x^{15} \] 2. **Raise the result to the power of 3**: \[ (x^{15})^3 = x^{15 \cdot 3} = x^{45} \] 3. **Now rewrite the whole expression**: \[ \frac{x^{45}}{x^2} \] 4. **Subtract the exponents in the denominator from the numerator**: \[ x^{45 - 2} = x^{43} \] Thus, the simplified expression is: \[ x^{43} \]