1 Tinh  

89/16+25(9/16÷125/64)÷(-27/8)

= \(\frac{89}{16}+25\left(\frac{9}{16}:\frac{125}{64}\right):-\frac{27}{8}\)

=\(\frac{89}{16}+\frac{25.36}{125}:-\frac{27}{8}\)

=\(\frac{89}{16}-\frac{32}{15}=\frac{823}{240}\)

\(\frac{89}{16}+25.\left(\frac{9}{16}:\frac{125}{64}\right):\left(\frac{-27}{8}\right)\)

=\(\frac{89}{16}+25.\frac{36}{125}:\left(\frac{-27}{8}\right)\)

=\(\frac{89}{16}+\frac{36}{5}:\left(\frac{-27}{8}\right)\)

=\(\frac{89}{16}+\left(\frac{-32}{15}\right)\)

=\(\frac{823}{240}\)

\(4\dfrac{25}{16}+25\left(\dfrac{9}{16}:\dfrac{125}{64}:\dfrac{-27}{8}\right)\)

\(=\dfrac{89}{16}+25\left(\dfrac{36}{125}:\dfrac{-27}{8}\right)\)

\(=\dfrac{89}{16}+25.\dfrac{-32}{375}\)

\(=\dfrac{89}{16}+\dfrac{-32}{15}=\dfrac{823}{240}\)

Chúc bạn học tốt!

\(4\dfrac{25}{16}+25\left(\dfrac{9}{16}:\dfrac{125}{64}:-\dfrac{27}{8}\right)\)

= \(\dfrac{89}{16}+25\left(\dfrac{9}{16}.\dfrac{64}{125}:-\dfrac{27}{8}\right)\)

= \(\dfrac{89}{16}+25\left(\dfrac{36}{125}:-\dfrac{27}{8}\right)\)

= \(\dfrac{89}{16}+25\left(\dfrac{36}{125}.-\dfrac{8}{27}\right)\)

= \(\dfrac{89}{16}+25.-\dfrac{32}{375}\)

\(=\dfrac{89}{16}+-\dfrac{32}{15}\)

= \(\dfrac{823}{240}\)

ai giúp mìn vứi ❤

\(=\frac{89}{16}+25.\frac{369}{500}:\left(\frac{-27}{8}\right)\)

\(=\frac{89}{16}+\frac{369}{20}:\left(\frac{-27}{8}\right)\)

\(=\frac{89}{16}+\frac{-82}{15}\)

\(=\frac{23}{240}\)

a, 2⁵ x 8⁴ =???

a)Ta có:

\(A=4\frac{25}{16}+25\left(\frac{9}{16}:\frac{125}{64}\right):\frac{-27}{8}\)

\(\Rightarrow A=\frac{89}{16}+25.\frac{36}{125}:\frac{-27}{8}\)

\(\Rightarrow A=\frac{89}{16}+\frac{36}{5}:\frac{-27}{8}\)

\(\Rightarrow A=\frac{89}{16}+\frac{-32}{15}\)

\(\Rightarrow A=\frac{823}{240}\)

Vậy A=.....

b)Ta có:

\(C=\frac{2^3}{3.5}+\frac{2^3}{5.7}+\frac{2^3}{7.9}+...+\frac{2^3}{101.103}\)

\(\Rightarrow C=\frac{2^2.2}{3.5}+\frac{2^2.2}{5.7}+\frac{2^2.2}{7.9}+...+\frac{2^2.2}{101.103}\)

\(\Rightarrow C=2^2\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{101.103}\right)\)

\(\Rightarrow C=4\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{101}-\frac{1}{103}\right)\)

\(\Rightarrow C=4\left(\frac{1}{3}-\frac{1}{103}\right)\)

\(\Rightarrow C=4.\frac{100}{309}\)

\(\Rightarrow C=\frac{400}{309}\)

Vậy C=.....

B, C=2^3/3.5 + 2^3/5.7+......+2^3/101.103

C= 2^3(1/3-1/5+1/5-1/7+....+1/101-1/103)

C=8(1/3-1/103)

C=8.100/309

C=800/309

VẬY C= 800/309

1) \(125^5:25^7\)

\(=\left(5^3\right)^5:\left(5^2\right)^7\)

\(=5^{15}:5^{14}\)

= 5

2) \(27^8:9^9\)

\(=\left(3^3\right)^8:\left(3^2\right)^9\)

\(=3^{24}:3^{18}\)

\(=3^6\)

3) \(36^5:6^8\)

\(=\left(6^2\right)^5:6^8\)

\(=6^{10}:6^8\)

\(=6^2\)

4) \(49^6:7^{10}\)

\(=\left(7^2\right)^6:7^{10}\)

\(=7^{12}:7^{10}=7^2\)

5) \(7^{20}:49^9\)

\(=7^{20}:\left(7^2\right)^9\)

\(=7^{20}:7^{18}=7^2\)

6) \(\frac{1}{2^{10}}:\frac{1}{8^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{\left(2^3\right)^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{2^9}=\frac{1}{2^{10}}.\frac{2^9}{1}=\frac{1}{2}\)

7) \(\left(-\frac{1}{2}\right)^{21}:\frac{1}{4^{10}}\)

\(=\frac{\left(-1\right)^{21}}{2^{21}}:\frac{1}{\left(2^2\right)^{10}}\)

\(=-\frac{1}{2^{21}}:\frac{1}{2^{20}}=-\frac{1}{2^{21}}.\frac{2^{20}}{1}\)

\(=-\frac{1}{2}\)

8) \(\frac{1}{16^5}:\left(-\frac{1}{2}\right)^{18}\)

\(=\frac{1}{\left(2^4\right)^5}:\frac{\left(-1\right)^{18}}{2^{18}}\)

\(=\frac{1}{2^{20}}:\frac{1}{2^{18}}\)

\(=\frac{1}{2^{20}}.\frac{2^{18}}{1}=\frac{1}{4}\)

9) \(\frac{1}{5^{30}}:\frac{1}{25^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{\left(5^2\right)^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{5^{28}}=\frac{1}{25}\)

\(9^7+81^4-27^5\)

\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)

\(=3^{14}+3^{16}-3^{15}\)

\(=3^{14}.\left(1+3^2-3\right)\)

\(=3^{14}.7⋮7\)

=> đpcm

\(25^{25}+5^{49}-125^{16}\)

\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)

\(=5^{50}+5^{49}-5^{48}\)

\(=5^{48}.\left(5^2+5-1\right)\)

\(=5^{48}.29⋮29\)

=> đpcm

              Bài làm :

\(\text{1) }9^7+81^4-27^5\)

\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)

\(=3^{14}+3^{16}-3^{15}\)

\(=3^{14}\left(1+3^2-3\right)\)

\(=3^{14}.7⋮7\)

=> Điều phải chứng minh

\(\text{2)}25^{25}+5^{49}-125^{16}\)

\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)

\(=5^{50}+5^{49}-5^{48}\)

\(=5^{48}\left(5^2+5-1\right)\)

\(=5^{48}.29⋮29\)

=> Điều phải chứng minh