(9a³b⁴)³/3a²b²×27a⁴b⁹=

To simplify the expression \((9a³b⁴)³/3a²b²×27a⁴b⁹\), we will follow these steps: 1. **Calculate \((9a³b⁴)³\)**: \[ (9a³b⁴)³ = 9³(a³)³(b⁴)³ = 729a^9b^{12} \] 2. **Rewrite the expression**: \[ \frac{729a^9b^{12}}{3a²b²} \times 27a^4b^9 \] 3. **Simplify the fraction \(\frac{729a^9b^{12}}{3a²b²}\)**: - Divide the coefficients: \(\frac{729}{3} = 243\) - Subtract the powers of \(a\): \(a^{9-2} = a^7\) - Subtract the powers of \(b\): \(b^{12-2} = b^{10}\) So, we have: \[ 243a^7b^{10} \] 4. **Now multiply by \(27a^4b^9\)**: \[ 243a^7b^{10} \times 27a^4b^9 \] - Multiply the coefficients: \(243 \times 27 = 6561\) - Add the powers of \(a\): \(a^{7+4} = a^{11}\) - Add the powers of \(b\): \(b^{10+9} = b^{19}\) So the final result is: \[ 6561a^{11}b^{19} \] Thus, the simplified expression is: \[ \boxed{6561a^{11}b^{19}} \]