5 mũ 2+4 mũ 9:4 mũ 3 .7 mũ3
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) \(\left(3^4.57-9^2.21\right):3^5\)
\(=\left(3^4.57-3^4.21\right):3^5\)
\(=\left[3^4\left(57-21\right)\right]:3^5\)
\(=3^4.36:3^5\)
\(=3^4.2^2.3^2:3^5\)
\(=3.4\)
\(=12\)
b) Ta có; \(1^3+2^3+...+9^3=2025\)
\(\Leftrightarrow2^3.\left(1^3+2^3+....+9^3\right)=2^3.2025\)
\(\Leftrightarrow2^3+4^5+...+18^3=16200\)
Ta có : C = 5 + 52 + 53 + 54 + ....... + 5100
=> 5C = 5. (5 + 52 + 53 + 54 + ....... + 5100)
=> 5C = 52 + 53 + 54 + ....... + 5101
=> 5C - C = 5101 - 5
=> 4C = 5101 - 5
=> C = \(\frac{5^{101}-5}{4}\)
\(C=5+5^2+5^3+5^4+...+5^{100}\)
\(5C=5^2+5^3+5^4+5^5+...+5^{101}\)
\(5C-C=\left(5^2+5^3+5^4+5^5+...+5^{101}\right)-\left(5+5^2+5^3+5^4+...+5^{100}\right)\)
\(4C=5^{101}-5\)
\(C\left(5^{101}-5\right):4\)
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)
5^2 + 4^9 : 4^3 . 7^3
= 5^2 + 4^9 : (4 . 7)^3
= 25 + 4^9 : 28^3
= 25 + 262144 : 21952
= 262169 : 21952
= 11.9428298105