Замените символ * степенью с основанием г так, чтобы выполнялось равенство:
а) $r^{12} ⋅ * ⋅ r^{3} ⋅ * = r^{26}$;
б) $r^{44} ⋅ * ⋅ r ⋅ * = r^{51}$;
в) $* ⋅ r^{7} ⋅ * ⋅ r^{9} ⋅ r^{13} = r^{48}$;
г) $r ⋅ r^{14} ⋅ * ⋅ r^{20} ⋅ * = r^{72}$.

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Решение

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ГДЗ учебник по алгебре 7 класс Мордкович. §17. Свойства степени с натуральными показателями. Номер №17.9.

Решение а

$r^{12} ⋅ * ⋅ r^{3} ⋅ * = r^{26}$
$* = r^{(26 - 12 - 3) : 2}$
$* = r^{11 : 2}$
$* = r^{5,5}$
$r^{12} ⋅ r^{5,5} ⋅ r^{3} ⋅ r^{5,5} = r^{26}$

Решение б

$r^{44} ⋅ * ⋅ r ⋅ * = r^{51}$
$* = r^{(51 - 44 - 1) : 2}$
$* = r^{6 : 2}$
$* = r^{3}$
$r^{44} ⋅ r^{3} ⋅ r ⋅ r^{3} = r^{51}$

Решение в

$* ⋅ r^{7} ⋅ * ⋅ r^{9} ⋅ r^{13} = r^{48}$
$* = r^{(48 - 7 - 9 - 13) : 2}$
$* = r^{19 : 2}$
$* = r^{9,5}$
$r^{9,5} ⋅ r^{7} ⋅ r^{9,5} ⋅ r^{9} ⋅ r^{13} = r^{48}$

Решение г

$r ⋅ r^{14} ⋅ * ⋅ r^{20} ⋅ * = r^{72}$
$* = r^{(72 - 1 - 14 - 20) : 2}$
$* = r^{37 : 2}$
$* = r^{18,5}$
$r ⋅ r^{14} ⋅ r^{18,5} ⋅ r^{20} ⋅ r^{18,5} = r^{72}$