\(\frac{13^5+13^4-13^3}{26^3}\)
\(=\frac{13^3\times(13^2+13-1)}{(2\times13)^3}\)
\(=\frac{13^3\times181}{2^3\times13^3}\)
\(=\frac{181}{8}\)
1) Tính :
\(\frac{13^5+13^4-13^3}{26^3}\)
\(=\frac{13^3.\left(13^2+13-1\right)}{13^3.2^3}\)
\(=\frac{13^3.181}{13^3.8}\)
\(=\frac{181}{8}\)
2) Ta có : 275 = 23.25 = (23)25 = 825
350 = 32.25 = (32)25 = 925
Vì 825 < 925 nên 275 < 350
=> 275 < 350
\(2^{75}=(2^3)^{25}=8^{25}\)
\(3^{50}=(3^2)^{25}=9^{25}\)
\(\Rightarrow8^{25}\)<\(9^{25}\)\(\Rightarrow2^{75}\)<\(3^{50}\)
\(2,2^{75}=\left(2^3\right)^{25}=8^{25}\)
\(3^{50}=\left(3^2\right)^{25}=9^{25}\)
\(\Rightarrow8^{25}< 9^{25}\)
\(\Leftrightarrow2^{75}< 3^{50}\)
275 = ( 23 )25 = 825
350 = ( 32 )25 = 925
Vì 8 < 9
=> 825 < 925
hay 275 < 350
