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Bài 6 trang 52 Tài liệu dạy – học toán 6 tập 1

Giải bài tập Tính cách lũy thừa sau và nêu nhận xét tổng quát.
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Đề bài

Tính cách lũy thừa sau và nêu nhận xét tổng quát. a) \({\left( {2.3} \right)^4}\)                                  b) \({\left( {a.b} \right)^5}\) c) \({\left( {{2^3}} \right)^2}\)                                   d) \({\left( {{a^5}} \right)^3}\).

Lời giải chi tiết

\(\eqalign{  & a)\;{\left( {2.3} \right)^4} = {6^4} = 1296  \cr  & b)\;{\left( {a.b} \right)^5} = (a.b).(a.b).(a.b).(a.b).(a.b) \cr&\;\;\;= (a.a.a.a.a).(b.b.b.b.b) = {a^5}.{b^5}  \cr  & c)\;{({2^3})^2} = {8^2} = 64  \cr  & d)\;{({a^5})^3} = {a^5}.{a^5}.{a^5} = {a^{15}} \cr} \)

Chúng ta nhận ra 1296 = 24.34. Như vậy ta có (2.3)4 = 24.34

Từ a) b) rút ra nhận xét tổng quát: Lũy thừa của một tích bằng tích các lũy thừa

Hơn nữa, ta còn có 64 = 26.

Nên (23)2 = 26 = 23.2

Từ c) d) rút ra nhận xét tổng quát: Khi tính lũy thừa của một lũy thừa, ta giữ nguyên cơ số và nhân hai số mũ.

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