(9а³b⁴)³|3a²b×27a⁴b⁹=

To solve the expression \((9a^3b^4)^3 | 3a^2b \times 27a^4b^9\), we will break it down step by step. 1. **Calculate \((9a^3b^4)^3\)**: \[ (9a^3b^4)^3 = 9^3(a^3)^3(b^4)^3 \] \[ 9^3 = 729, \quad (a^3)^3 = a^{9}, \quad (b^4)^3 = b^{12} \] Therefore, \[ (9a^3b^4)^3 = 729a^9b^{12} \] 2. **Calculate \(3a^2b \times 27a^4b^9\)**: \[ 3a^2b \times 27a^4b^9 = (3 \times 27)(a^2 \times a^4)(b \times b^9) \] \[ 3 \times 27 = 81, \quad a^2 \times a^4 = a^{2+4} = a^6, \quad b \times b^9 = b^{1+9} = b^{10} \] Therefore, \[ 3a^2b \times 27a^4b^9 = 81a^6b^{10} \] 3. **Combine the two parts**: Now we have: \[ 729a^9b^{12} | 81a^6b^{10} \] If the '|' indicates division, we calculate: \[ \frac{729a^9b^{12}}{81a^6b^{10}} \] Simplifying: \[ = \frac{729}{81} \cdot \frac{a^9}{a^6} \cdot \frac{b^{12}}{b^{10}} = 9 \cdot a^{9-6} \cdot b^{12-10} = 9a^3b^2 \] Thus, the final result is: \[ \boxed{9a^3b^2} \]