Найдите показатели степеней выражений для всех чисел \(\displaystyle a,\, z,\, x\) и \(\displaystyle t\):
| \(\displaystyle (a+8z)\!\cdot\! (xt)\!\cdot\! (a+8z)\!\cdot\! (a+8z)\!\cdot\! (xt)\!\cdot\! (a+8z)\!\cdot\! (xt)\!\cdot\! (xt)\!=\!(a+8z)\) | \(\displaystyle \!\cdot\! \,(xt)\) |
Так как в произведении
\(\displaystyle \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{blue}{(a+8z)}\cdot \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{red}{(xt)}\)
\(\displaystyle (a+8z)\) повторяется \(\displaystyle {\bf \color{blue}4}\) раза,
\(\displaystyle (xt)\) повторяется \(\displaystyle {\bf \color{red}4}\) раза,
то
\(\displaystyle \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{blue}{(a+8z)}\cdot \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{blue}{(a+8z)}\cdot \color{red}{(xt)}\cdot \color{red}{(xt)}= (a+8z)^{\bf \color{blue} 4}\cdot (xt)^{\bf \color{red}4}.\)
Ответ: \(\displaystyle (a+8z)^4 \cdot (xt)^4.\)