Question

bài 1: tính

a) \(\left(\frac{3}{7}\right)^0=\frac{7}{9}:\left(\frac{2}{3}\right)^2-\left|-\frac{4}{5}\right|\)

b) \(\frac{10^3+2.5^3+5^3}{55}\)

bài 2: so sánh

\(^{3^{2009}}\) và \(9^{1005}\)  

thanksss~~~

Answer 1

a.

\(\left(\frac{3}{7}\right)^0+\frac{7}{9}\div\left(\frac{2}{3}\right)^2-\left|-\frac{4}{5}\right|=0+\frac{7}{9}\div\frac{4}{9}-\frac{4}{5}=\frac{7}{9}\times\frac{9}{4}-\frac{4}{5}=\frac{7}{4}-\frac{4}{5}=\frac{35}{20}-\frac{16}{20}=\frac{19}{20}\)

b.

\(\frac{10^3+2\times5^3+5^3}{55}=\frac{\left(2\times5\right)^3+2\times5^3+5^3}{55}=\frac{2^3\times5^3+2\times5^3+5^3}{5\times11}=\frac{5^3\times\left(2^3+2+1\right)}{5\times11}=\frac{5^2\times11}{11}=5^2=25\)

c.

\(3^{2009}< 3^{2010}=\left(3^2\right)^{1005}=9^{1005}\)

Vậy 3²⁰⁰⁹ < 9¹⁰⁰⁵

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