a. \(\frac{20^5.5^{10}}{100^5}\)

\(=\frac{20^5.\left(5^2\right)^5}{100^5}\)

\(=\frac{20^5.25^5}{100^5}\)

\(=\frac{500^5}{100^5}\)

\(=\left(\frac{500}{100}\right)^5\)

\(=5^5=3125\)

b. \(\frac{\left(0,9\right)^5}{\left(0,3\right)^6}\)

\(=\frac{\left(0,9\right)^5}{\left(0,3\right)^5.0,3}\)

\(=\left(\frac{0,9}{0,3}\right)^5.\frac{1}{0,3}\)

\(=3^5.\frac{1}{0,3}\)

\(=810\)

c. \(\frac{6^3+3.6^2+3^3}{-13}\)

\(=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}\)

\(=\frac{3^3\left(2^3+2^2+1\right)}{-13}\)

\(=\frac{3^3.13}{-13}\)

\(=\left(-3\right)^3\)

\(=-27\)

d)\(\frac{6^3+3\cdot6^2+3^3}{-13}=\frac{3^3\cdot2^3+3^3\cdot2^2+3^3}{-13}=\frac{3^3\left(8+4+1\right)}{-13}=\frac{3^3\cdot13}{-13}=-27\)

giang làm a,b,c rồi nên làm d thôi

lười quá, hehe ^_^

a) \(\frac{4^2\cdot4^3}{2^{10}}=\frac{\left(2^2\right)^2.\left(2^2\right)^3}{2^{10}}=\frac{2^4.2^6}{2^{10}}=\frac{2^{10}}{2^{10}}=1\)

b)\(\frac{\left(0,6\right)^5}{\left(0,2\right)^6}=\frac{\left(0,2.3\right)^5}{\left(0,2\right)^6}=\frac{\left(0,2\right)^5.3^5}{\left(0,2\right)^6}=\frac{3^5}{0,2}=\frac{243.5}{1}=1215\)

c)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{2^7.3^5}{2^{11}.3^5}=\frac{1}{2^4}=\frac{1}{16}\)

nhanh lên nhé

(1+\(\frac{1}{3}\)) x (1+\(\frac{1}{2x4}\)) x(1+\(\frac{1}{3x5}\))x(1+\(\frac{1}{4x6}\)) x .....x (1+ \(\frac{1}{2009x2011}\))

= \(\frac{2}{1x3}\)x \(\frac{2}{2x4}\)x \(\frac{2}{3x5}\)x \(\frac{2}{4x6}\)x....x \(\frac{2}{2009x2011}\)

= ..................

đến đây tự làm nhé

làm hết đi mà

\(\frac{59}{10}:\frac{3}{2}-\left(\frac{7}{3}\cdot\frac{17}{4}-28\cdot\frac{4}{3}\right):\frac{7}{4}\)

\(=\frac{59}{15}-\frac{29}{4}:\frac{7}{4}=\)\(\frac{59}{15}-\frac{29}{7}=\frac{-22}{105}\)

B = \(\frac{59}{10}:\frac{3}{2}-\left(\frac{7}{3}x\frac{17}{4}-2x\frac{4}{3}\right):\frac{7}{4}\)

    = \(\frac{59}{10}x\frac{2}{3}-\left(\frac{119}{12}-\frac{8}{3}\right)x\frac{4}{7}\)

    = \(\frac{59}{15}-\frac{29}{4}x\frac{4}{7}=\frac{59}{15}-\frac{29}{7}\)

     = \(\frac{-22}{105}\)

C = \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)

    = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

     = \(1-\frac{1}{7}=\frac{6}{7}\)

\(B=\frac{59}{15}-\frac{29}{7}\)

 \(=\frac{-22}{105}\) ( bài B này mk hk pít giải nhanh mk bấm máy tính lụi)

\(C=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)\(\left(vì\frac{1}{1.2}=\frac{1}{1}-\frac{1}{2}\right)\)

\(C=1-\frac{1}{7}=\frac{6}{7}\)

a, 1

b, 1215

c, \(\frac{3}{16}\)

d, \(\frac{3132}{-13}\)