(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: \[ \boxed{6561a^{11}b^{19}} \]