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Задача Задача №2130520
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Аноним
07 ноября 2024 11:13 · публичный вопрос
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Аноним

18х3у2z*(-2/9xy2zx2)*(-2xyzxyx)=

Ответ нейросети
07 ноября 2024 11:13

To simplify the expression \( 18x^3y^2z \cdot \left(-\frac{2}{9}xy^2zx^2\right) \cdot (-2xyzxyx) \), we'll multiply everything together step by step, focusing on both numerical coefficients and variables.

  1. Multiply the coefficients: \[ 18 \cdot \left(-\frac{2}{9}\right) \cdot (-2) = 18 \cdot \left(-\frac{2 \cdot -2}{9}\right) = 18 \cdot \frac{4}{9} \]

    To simplify \( 18 \cdot \frac{4}{9} \): \[ 18 = 2 \cdot 9 \quad \Rightarrow \quad \frac{18}{9} = 2 \] \[ 2 \cdot 4 = 8 \]

  2. Multiply the variables: \[ x^3 \cdot x \cdot x = x^{3+1+1} = x^5 \] \[ y^2 \cdot y^2 \cdot y \cdot y = y^{2+2+1+1} = y^6 \] \[ z \cdot z \cdot z = z^{1+1+1} = z^3 \]

  3. Combine all together: Now that we have the coefficient and the powers of the variables, we put everything together: \[ 8x^5y^6z^3 \]

Thus, the simplified expression is: \[ \boxed{8x^5y^6z^3} \]