Question

a/10^4.4^2.25^3/20^2.4.5

b/18^3.27.8^2/9^2.6^2.3^2

c/4/5.(1-1/2)^2-1/4.2/5+6/5.3/4

d/(4-1/3)^2:1/5-5.[2/3-(1/3)^2]

Answer 1

a: \(\dfrac{10^4\cdot4^2\cdot25^3}{20^2\cdot4\cdot5}=\dfrac{2^4\cdot5^4\cdot2^4\cdot5^6}{20^3}=\dfrac{2^8\cdot5^{10}}{5^3\cdot2^6}=2^2\cdot5^7\)

b: \(\dfrac{18^3\cdot27\cdot8^2}{9^2\cdot6^2\cdot3^2}=\dfrac{\left(3^2\cdot2\right)^3\cdot3^3\cdot2^6}{3^4\cdot3^2\cdot2^2\cdot3^2}\)

\(=\dfrac{3^6\cdot2^3\cdot3^3\cdot2^6}{3^8\cdot2^2}=\dfrac{3^{15}}{3^8}\cdot2=3^7\cdot2\)

c: \(\dfrac{4}{5}\left(1-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\cdot\dfrac{2}{5}+\dfrac{6}{5}\cdot\dfrac{3}{4}\)

\(=\dfrac{4}{5}\cdot\dfrac{1}{4}-\dfrac{1}{10}+\dfrac{3}{2}\cdot\dfrac{3}{5}\)

\(=\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{9}{10}=\dfrac{1}{5}+\dfrac{4}{5}=1\)

d: \(\left(4-\dfrac{1}{3}\right)^2:\dfrac{1}{5}-5\left[\dfrac{2}{3}-\left(\dfrac{1}{3}\right)^2\right]\)

\(=\left(\dfrac{11}{3}\right)^2\cdot5-5\left[\dfrac{2}{3}-\dfrac{1}{9}\right]\)

\(=\dfrac{121}{9}\cdot5-5\cdot\dfrac{5}{9}\)

\(=5\left(\dfrac{121}{9}-\dfrac{5}{9}\right)=5\cdot\dfrac{116}{9}=\dfrac{580}{9}\)