Question

4.9. Докажите тождество: 1) (a²)4 . (a³)5 : (a³)7 = a²; 2) (x³)6. (x²)5 = x²8​

Answer 1

$\displaystyle\bf\\1)\\\\\Big(a^{2} \Big)^{4} \cdot\Big(a^{3} \Big)^{5} :\Big(a^{3} \Big)^{7} =a^{2\cdot 4} \cdot a^{3\cdot 5} :a^{3\cdot 7} =a^{8} \cdot a^{15} :a^{21} =a^{8+15-21} =a^{2} \\\\\\2)\\\\\Big(x^{3} \Big)^{6} \cdot\Big(x^{2} \Big)^{5} =x^{3\cdot 6} \cdot x^{2\cdot 5} =x^{18} \cdot x^{10} =x^{18+10} =x^{28}$