[tex]\displaystyle\bf\\1)\\\\\Big(a^{4} \Big)^{2n} \cdot\Big(a^{n} \cdot a^{n+2} \Big)^{2} =a^{4\cdot 2n} \cdot\Big( a^{n+n+2} \Big)^{2} =a^{8n} \cdot\Big(a^{2n+2} \Big)^{2} =\\\\\\=a^{8n} \cdot a^{4n+4} =a^{8n+4n+4} =a^{12n+4} \\\\2)\\\\\Big((-x)^{n}\Big)^{3} \cdot\Big((-x)^{n+1} \Big)^{5} =(-x)^{3n} \cdot (-x)^{5n+5} =\\\\\\=(-x)^{3n+5n+5} =(-x)^{8n+5}[/tex]