[tex]\displaystyle\bf\\a)\\2^4\cdot3^2-2^4=2^4(3^2-1)=2^4(9-1)=2^4\cdot8=2^4\cdot2^3=2^{4+3}=\boxed{\bf2^7}\\\\b)\\7^5\cdot7^6\cdot7-7^3\cdot7^6\cdot7^2\cdot7=7^{5+6+1}-7^{3+6+2+1}=7^{12}-7^{12}=\boxed{0}\\\\c)\\\Big(5^3\Big)^4:5^{11}=5^{3\times4}:5^{11}=5^{12}:5^{11}=5^{12-11}=\boxed{\bf5^1}\\\\d)\\\Big(2^3\Big)^5:\Big(2^4\Big)^3=2^{3\times5}:2^{4\times3}=2^{15}:2^{12}=2^{15-12}=\boxed{\bf2^3}[/tex]
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[tex]\displaystyle\bf\\e)\\\Big(1+3^{14}:3^9\Big):\Big(1+3^4\cdot3^2:3\Big)=\\\\=\Big(1+3^{14-9}\Big):\Big(1+3^{4+2-1}\Big)=\Big(1+3^5\Big):\Big(1+3^5\Big)=\boxed{\bf1}[/tex]
