1.
6 - 2х² = 6 - 2(-8)² = 6 - 2(64) = 6 - 128 = -122
2.
[tex]\displaystyle\tt a^{11}\cdot a^{14}=a^{11+14}=a^{25}\\\\a^{18}:a^{14}=a^{18-14}=a^4\\\\(a^5)^4=a^{5\cdot4}=a^{20}\\\\(5x)^4=5^4\cdot x^4=625x^4\\\\\bigg(\frac{a}{3}\bigg)^6=\frac{a^6}{3^6}=\frac{a^6}{729}[/tex]
3.
[tex]\displaystyle\tt \frac{14^{16}\cdot14^{6}}{14^{21}}=14^{16+6-21}=14^1=14\\\\\\ \frac{7^{8}\cdot7^{5}}{7^{11}}=7^{8+5-11}=7^2=49\\\\\\ (12^2-11^2)^2+(6^5+2^9)^0=(144-121)^2+1=23^2+1=529+1=530[/tex]
4.
[tex]\displaystyle\tt 3^{8x}=81\\\\3^{8x}=3^4\\\\8x=4\\\\x=\frac{4}{8}=\frac{1}{2}=0.5[/tex]
5.
[tex]\displaystyle\tt \frac{64^{6}}{4^{4}\cdot4^{16}}=\frac{(4^3)^{6}}{4^{4+16}}=\frac{4^{3\cdot6}}{4^{20}}=\frac{4^{18}}{4^{20}}=\frac{1}{4^{2}}=\frac{1}{16}[/tex]
