B1.Chứng minh rằng :
a. \(5^5-5^4+5^3⋮7\)
b.\(7^6+7^5-7^4⋮11\)
c.\(24^{54}.54^{24}.2^{10}⋮72^{63}\)
B2.Tìm các số nguyên dương n biết :
a.\(32< 2^n< 128\)
b.\(9.27\le3^n\le243\)
B3. Rút gọn biểu thức ( Tính )
a.\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
b.\(\dfrac{4^6.9^5+6^9.120}{\left(-8^4\right).3^{12}-6^{11}}\)
Bài 1:
\(a.5^5-5^4+5^3\)
\(=5^3.5^2-5^3.5+5^3.1\)
\(=5^3\left(5^2-5+1\right)\)
\(=5^3.21\)
\(=5^3.3.7⋮7\)
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Bài 2:
\(a.32< 2^n< 128\)
\(\Rightarrow2^5< 2^n< 2^7\)
\(\Rightarrow n=2\)
\(b.9.27\le3^n\le243\)
\(\Rightarrow3^2.3^3\le3^n\le3^5\)
\(\Rightarrow3^5\le3^n\le3^5\)
\(\Rightarrow n=5\)
Bài 3
\(a.\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
\(=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}\)
\(=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(=\dfrac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}\)
\(=\dfrac{2^{10}.3^8.\left(-2\right)}{2^{10}.3^8.6}\)
\(=\dfrac{-2}{6}\)
\(=\dfrac{-1}{3}\)
Câu b bạn tự làm nha
đưa về lũy thừa có cơ số là 2,3 như câu a rồi rút gọn
