d)

\(\dfrac{3^9.3^{20}.2^8}{3^{24}.243.2^6}\\ =\dfrac{3^{29}.2^6.2^2}{3^{24}.3^5.2^6}\\ =\dfrac{3^{29}.2^6.4}{3^{29}.2^6}\\ =4\)

e)

\(\dfrac{2^{15}.5^3.2^6.3^4}{8.2^{18}.81.5}\\ =\dfrac{2^{21}.5^3.3^4}{2^3.2^{18}3^4.5}\\ =\dfrac{2^{21}.5.5^2.3^4}{2^{21}.3^4.5}\\ =5^2\\ =25\)

f)

\(=\dfrac{24\left(315+561+124\right)}{\dfrac{\left(1+99\right).50}{2}-500}\\ =\dfrac{24.1000}{2500-500}\\ =12\)

\(a,\dfrac{-14.15}{21.\left(-10\right)}=\dfrac{-7.2.3.5}{7.3.\left(-2\right).5}=1\)

\(b,\dfrac{5.7-7.9}{7.2+6.7}=\dfrac{7\left(5-9\right)}{7\left(2+6\right)}=\dfrac{-4}{8}=-\dfrac{1}{2}\)

\(c,\dfrac{\left(-7\right).3+2.\left(-14\right)}{\left(-5\right).7-2.7}=\dfrac{-7.\left(3+4\right)}{7\left(-5-2\right)}\)

\(=\dfrac{\left(-7\right).7}{7.\left(-7\right)}=1\)

\(d,\dfrac{3^9.3^{20}.2^8}{3^{24}.243.2^6}=\dfrac{3^{29}.2^8}{3^{24}.3^5.2^6}=\dfrac{3^{29}.2^8}{3^{29}.2^6}=2^2=4\)

\(e,\dfrac{2^{15}.5^3.2^6.3^4}{8.2^{18}.81.5}=\dfrac{2^{21}.3^4.5^3}{2^{18}.2^3.3^4.5}=\dfrac{2^{21}.3^4.5^3}{2^{21}.3^4.5}=5^2=25\)

\(f,\dfrac{24.315+3.561.8+4.124.6}{1+3+5+...+97+99-500}\)

\(=\dfrac{24.315+24.561+24.124}{1+3+5+...+97+99-500}\)

\(=\dfrac{24\left(315+561+124\right)}{1+3+5+...+97+99-500}\)

\(=\dfrac{24.1000}{1+3+5+...+97+99-500}\) (1)

Đặt A = 1 + 3 + 5 + ... + 97 + 99

Số số hạng trong A là: (99 - 1) : 2 + 1 = 50 (số)

Tổng A bằng: (99 + 1) . 50 : 2 = 2500

Thay A = 2500 vào biểu thức (1), ta được:

\(\dfrac{24.1000}{2500-500}=\dfrac{24.1000}{2.1000}=12\)

a. \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\frac{15}{13.2}-\frac{2}{13}=\frac{15}{13.2}-\frac{2.2}{13.2}=\frac{15-4}{26}=\frac{11}{26}\)

C. \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{1}{23}.\left(-11.\frac{6}{7}-11.\frac{8}{7}-1\right)=\frac{1}{23}.\left(-22-1\right)=\frac{1}{23}.\left(-23\right)=-1\)

a) \(M=\left(71+x\right)-\left(-24-x\right)+\left(-35-x\right)\)

\(=71+x-\left(-24\right)+x+\left(-35\right)-x\)

\(=60+x\)

b) \(x-34-\left[\left(15+x\right)-\left(23-x\right)\right]\)

\(=x-34-\left(15+x-23+x\right)\)

\(=x-34-\left(-8+2x\right)\)

\(=x-34-\left(-8\right)-2x\)

\(=-26-x\)

c) \(\left(-15+\left|x\right|\right)+\left(25-\left|x\right|\right)\)

\(=-15+\left|x\right|+25-\left|x\right|\)

\(=10\)

Cách 1:

a) \(12:6 = 2\)

b) \(24:\left( { - 8} \right)=-(24:8)=-3\)

c) \(\left( { - 36} \right):9=-(36:9)=-4\)

d) \(\left( { - 14} \right):\left( { - 7} \right)=14:7=2\)

Cách 2:

a) Ta có \(12 = 6.2\) nên \(12:6 = 2\).

b) Ta có \(24 = \left( { - 8} \right).\left( { - 3} \right)\)\( \Rightarrow 24:\left( { - 8} \right) = \left( { - 3} \right)\).

c) Ta có \(\left( { - 36} \right) = 9.\left( { - 4} \right)\) nên \(\left( { - 36} \right):9 = \left( { - 4} \right)\).

d) Ta có \(\left( { - 14} \right) = \left( { - 7} \right).2\) nên \(\left( { - 14} \right):\left( { - 7} \right) = 2\)

a) Số trừ là \(9\) có số đối là \(\left( { - 9} \right)\) nên ta có:

\(6 - 9 = 6 + \left( { - 9} \right) =  - \left( {9 - 6} \right) =  - 3\)

b) Số trừ là \(\left( { - 12} \right)\) có số đối là \(12\) nên ta có:

\(23 - \left( { - 12} \right) = 23 + 12 = 35\)

c) Số trừ là \(\left( { - 60} \right)\) có số đối là \(60\) nên ta có:

\(\begin{array}{l}\left( { - 35} \right) - \left( { - 60} \right) = \left( { - 35} \right) + 60\\ = 60 - 35 = 25\end{array}\)

d) Số trừ là \(53\) có số đối là \(\left( { - 53} \right)\) nên ta có:

\(\begin{array}{l}\left( { - 47} \right) - 53 = \left( { - 47} \right) + \left( { - 53} \right)\\ =  - \left( {47 + 53} \right) =  - 100\end{array}\)

e) Số trừ là \(\left( { - 43} \right)\) có số đối là 43 nên ta có:

\(\left( { - 43} \right) - \left( { - 43} \right) = \left( { - 43} \right) + 43 = 0\).

a) \(\dfrac{-3}{7}+\dfrac{15}{26}-\left(\dfrac{2}{13}-\dfrac{3}{7}\right)\\ =\dfrac{-3}{7}+\dfrac{15}{26}-\dfrac{2}{13}+\dfrac{3}{7}\\ =\left(\dfrac{-3}{7}+\dfrac{3}{7}\right)+\left(\dfrac{15}{26}-\dfrac{2}{13}\right)\\ =0+\left(\dfrac{15}{26}-\dfrac{4}{26}\right)\\ =0+\dfrac{11}{26}\\ =\dfrac{11}{26}\)

\(c)\dfrac{-11}{23}.\dfrac{6}{7}+\dfrac{8}{7}.\dfrac{-11}{23}-\dfrac{1}{23}\\=\dfrac{-1}{23}\left ( \dfrac{66}{7}+\dfrac{88}{7}+1 \right )\\ =\dfrac{-1}{23}.23=-1\)

a) \(\left( { - 3} \right).7 =  - \left( {3.7} \right) =  - 21\)

b) \(\left( { - 8} \right).\left( { - 6} \right) = 8.6 = 48\)

c) \(\left( { + 12} \right).\left( { - 20} \right) =  - \left( {12.20} \right) =  - 240\)

d) \(24.\left( { + 50} \right) = 24.50 = 1200\)