Thay dấu “?” bằng số thích hợp:
a)\({\left( {\dfrac{2}{3}} \right)^5}.{\left( {\dfrac{2}{3}} \right)^?} = {\left( {\dfrac{2}{3}} \right)^8};\)
b)\({\left( { – \dfrac{3}{4}} \right)^?}:{\left( {\dfrac{{ – 3}}{4}} \right)^7} = {\left( {\dfrac{{ – 3}}{4}} \right)^2}\)
Áp dụng nhân, chia hai luỹ thừa cùng cơ số
a)
\(\begin{array}{l}{\left( {\dfrac{2}{3}} \right)^5}.{\left( {\dfrac{2}{3}} \right)^?} = {\left( {\dfrac{2}{3}} \right)^8}\\ \Rightarrow {\left( {\dfrac{2}{3}} \right)^{5 + ?}} = {\left( {\dfrac{2}{3}} \right)^8}\\ \Rightarrow 5 + ? = 8\\ \Rightarrow ? = 8 – 5\\ \Rightarrow ? = 3\end{array}\)
Vậy \(? =3\)
b)
\(\begin{array}{l}{\left( { – \dfrac{3}{4}} \right)^?}:{\left( {\dfrac{{ – 3}}{4}} \right)^7} = {\left( {\dfrac{{ – 3}}{4}} \right)^2}\\ \Rightarrow {\left( { – \dfrac{3}{4}} \right)^{? – 7}} = {\left( { – \dfrac{3}{4}} \right)^2}\\ \Rightarrow ? – 7 = 2\\ \Rightarrow ? = 2 + 7\\ \Rightarrow ? = 9\end{array}\)
Vậy \(? =9\)