Đề bài

Viết kết quả mỗi phép tính sau dưới dạng một lũy thừa: a) \({3^4}{.3^5}\);     \({16.2^9}\);    \(16.32\); b) \({12^8}:12\);  \(243:{3^4}\);  \({10^9}:10000\). c) \({4.8^6}{.2.8^3}\);  \({12^2}{.2.12^3}.6\);  \({6^3}{.2.6^4}.3\).

Lời giải chi tiết

a) Ta có: \({3^4}{.3^5} = {3^{4 + 5}} = {3^9}\);      Ta có: \(16 = 2.2.2.2 = {2^4}\). \(\Rightarrow\) \({16.2^9} = {2^4}{.2^9} = {2^{4 + 9}} = {2^{13}}\);  Ta có: \(32 = 2.2.2.2.2 = {2^5}\) \(\Rightarrow\) \(16.32 = {2^4}{.2^5} = {2^{4 + 5}} = {2^9}\) b) \({12^8}:12 = {12^8}:{12^1} = {12^{8 - 1}} = {12^7}\); Ta có: \(243 = 3.3.3.3.3 = {3^5}\) \(\Rightarrow 243:{3^4} = {3^5}:{3^4} = {3^{5 - 4}} = {3^1} = 3\). Ta có: \(10000 = {10^4}\) \(\Rightarrow\)\({10^9}:10000 = {10^9}:{10^4} = {10^{9 - 4}} = {10^5}\) c) \(\begin{array}{l}{4.8^6}{.2.8^3} = {4.2.8^6}{.8^3}\\ = \left( {4.2} \right){.8^6}{.8^3}\\ = {8.8^6}{.8^3}\\ = {8^1}{.8^6}{.8^3}\\ = {8^{1 + 6 + 3}} = {8^{10}}\end{array}\) \(\begin{array}{l}{12^2}{.2.12^3}.6\\ = {12^2}{.12^3}.\left( {2.6} \right)\\ = {12^2}{.12^3}.12\\ = {12^{2 + 3 + 1}} = {12^6}\end{array}\) \(\begin{array}{l}{6^3}{.2.6^4}.3\\ = {6^3}{.6^4}.\left( {2.3} \right)\\ = {6^3}{.6^4}.6\\ = {6^{3 + 4 + 1}}\\ = {6^8}\end{array}\)

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