bài này không khó. Nhưng đánh máy để giải cho bạn thì thực sự khó

a) \(\left|\frac{-15}{6}\right|-\left|\frac{3}{18}\right|.\sqrt{81}+\sqrt{\frac{9}{64}}\)

\(=\frac{15}{6}-\frac{1}{6}.9+\frac{3}{8}\)

\(=\frac{15}{6}-\frac{9}{6}+\frac{3}{8}\)

\(=1+\frac{3}{8}\)

\(=\frac{11}{8}\)

b) \(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}=\frac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}=\frac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}=2^2.3=12\)

a/ \(\left|\frac{-15}{6}\right|-\left|\frac{3}{18}\right|.\sqrt{81}+\sqrt{\frac{9}{64}}\)

= \(\frac{15}{6}-\frac{3}{18}.9+\frac{8}{8}\)

= \(\frac{15}{6}-\frac{3}{2}+\frac{3}{8}\)

= \(\frac{60-36+9}{24}=\frac{33}{24}=\frac{11}{8}\)

b/ \(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}=\frac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}\) \(=\frac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}=\frac{2^2.3^{35}}{3^{34}}=\frac{4.3}{1}=12\)

Bài 1:

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + (\(\frac45\) - \(\frac{3}{17}\) + \(\frac13\)) - \(\frac17\) + (- \(\frac{14}{30}\))

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + \(\frac45\) - \(\frac{3}{17}\) + \(\frac13\) - \(\frac17\) - \(\frac{14}{30}\)

A = (\(\frac15\) + \(\frac45\)) + (\(\frac{3}{17}\) - \(\frac{3}{17}\)) - (\(\frac43-\frac13\)) - \(\frac{30}{210}\) - \(\frac{98}{210}\)

A = 1 + 0 - 1 - (\(\frac{30}{210}+\frac{98}{210}\))

A = 1 - 1 - \(\frac{228}{210}\)

A = 0 - \(\frac{128}{210}\)

A = - \(\frac{64}{105}\)

Bài 2:

B= (\(\frac58\) - \(\frac{4}{12}\) + \(\frac32\)) - (\(\frac58\) + \(\frac{9}{13}\)) - (\(\frac{-3}{2}\)) + \(\frac{7}{-15}\)

B = \(\frac58\) - \(\frac{4}{12}\) + \(\frac32\) - \(\frac58\) - \(\frac{9}{13}\) + \(\frac32\) - \(\frac{7}{15}\)

B = (\(\frac58\) - \(\frac58\)) + (\(\frac32\) + \(\frac32\)) - (\(\frac13\) + \(\frac{9}{13}\) + \(\frac{7}{15}\))

B = 0 + 3 - (\(\frac{65}{195}\) + \(\frac{135}{195}\) + \(\frac{91}{195}\))

B = 3 - (\(\frac{200}{195}\) + \(\frac{91}{195}\))

B = 3 - \(\frac{97}{65}\)

B = \(\frac{195}{65}\) - \(\frac{97}{65}\)

B = \(\frac{98}{65}\)

(3\(x\) - \(\frac{2}{15}\))\(^3\) = \(\frac{8}{125}\)

(3\(x\) - \(\frac{2}{15}\))\(^3\) = (\(\frac25\))\(^3\)

3\(x\) - \(\frac{2}{15}\) = \(\frac25\)

3\(x\) = \(\frac25\) + \(\frac{2}{15}\)

3\(x\) = \(\frac{6}{15}\) + \(\frac{2}{15}\)

3\(x\) = \(\frac{8}{15}\)

\(x\) = \(\frac{8}{15}\) : 3

\(x\) = \(\frac{8}{15}\) x \(\frac13\)

\(x=\frac{8}{45}\)

Vậy \(x=\frac{8}{45}\)

a: \(\frac{4^{30}\cdot3^{43}}{2^{53}\cdot27^{15}}\)

\(=\frac{\left(2^2\right)^{30}\cdot3^{43}}{2^{53}\cdot\left(3^3\right)^{15}}\)

\(=\frac{2^{60}}{2^{53}}\cdot\frac{3^{43}}{3^{45}}=\frac{2^7}{3^2}=\frac{128}{9}\)

b: \(\left(-27\right)^{10}\cdot16^{25}\)

\(=-3^{30}\cdot\left(2^4\right)^{25}=-3^{30}\cdot2^{100}\)

\(6^{30}\cdot\left(-32\right)^{15}\)

\(=2^{30}\cdot3^{30}\cdot\left(-1\right)\cdot\left(2^5\right)^{15}=-2^{105}\cdot3^{30}\)

\(\frac{\left(-27\right)^{10}\cdot16^{25}}{6^{30}\cdot\left(-32\right)^{15}}\)

\(=\frac{-2^{100}\cdot3^{30}}{-2^{105}\cdot3^{30}}=\frac{1}{2^5}=\frac{1}{32}\)

c: \(\left(-\frac{2}{17}\right)^3\cdot\left(-\frac{17}{35}\right)^3\cdot\left(\frac{35}{3}\right)^3\)

\(=\left(-\frac{2}{17}\cdot\frac{-17}{35}\cdot\frac{35}{3}\right)^3\)

\(=\left(\frac23\right)^3=\frac{8}{27}\)

e: \(2^2+4^2+\cdots+24^2\)

\(=2^2\left(1^2+2^2+\cdots+12^2\right)\)

\(=4\cdot650=2600\)

Cũng khuya rồi , mình làm câu 1 thôi nhé !
\(\frac{2.5^{22}-9.5^{21}}{25^{10}}=\frac{2.5^{22}-9.5^{21}}{\left(5^2\right)^{10}}\)
\(\frac{5^{21}.\left(2.5-9\right)}{5^{20}}=5.\left(10-9\right)=5\)
 

a, Tự chép đề bài ((:

\(=\frac{1}{9}\cdot1+\left(-\frac{1}{243}\right)\cdot\frac{9}{2}\)

\(=\frac{1}{9}-\frac{1}{54}\)

\(=\frac{5}{54}\)

b, 1. \(\left(\frac{2^2\cdot2^3}{4^2\cdot16}\right)^{15}\)

\(=\left(\frac{2^5}{2^4\cdot2^4}\right)^5=\left(\frac{2^5}{2^8}\right)^5=\left(\frac{1}{2^3}\right)^5=\left(\frac{1}{8}\right)^5=\frac{1}{8^5}\)(Để vậy đi :v)

     2. \(\left(\frac{2^6}{16^2}\right)^{10}\)

\(=\left(\frac{2^6}{2^8}\right)^{10}=\left(\frac{1}{2^2}\right)^{10}=\frac{1}{2^{20}}\)

c, \(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}\)

\(=\frac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}=\frac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\frac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=\frac{3^2}{1}=3^2=9\)