\(\frac{17}{-26}.\left(\frac{1}{6}-\frac{1}{5}\right):\frac{17}{13}-\frac{20}{3}.\left(\frac{2}{5}-\frac{1}{4}\right)+\frac{2}{3}.\left(\frac{6}{5}-\frac{9}{2}\right)\)

\(=\frac{17}{13}:\left(-2\right).\frac{-1}{30}.\frac{13}{17}-\frac{20}{3}.\frac{3}{20}+\frac{2}{3}.\frac{-33}{10}\)

\(=\left(\frac{17}{13}.\frac{13}{17}\right).\left[\frac{-1}{30}:\left(-2\right)\right]-1+\frac{-11}{5}\)

\(=1.\frac{1}{60}-1-\frac{11}{5}\)\(=\frac{-191}{60}\)

\(2x=3y=5z\Leftrightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có: 

\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x+2y+z}{15+2.10+6}=\frac{41}{41}=1\)

\(\Leftrightarrow\hept{\begin{cases}x=1.15=15\\y=1.10=10\\z=1.6=6\end{cases}}\)

Đáp án:

a) Góc D1= 75 độ (đối đỉnh)

Góc DCy+ góc ADC =180 độ

Góc DCy+ 75 dộ= 180 độ

=> Góc DCy=180 độ-75 độ= 105 độ

\(\frac{17}{-26}.\left(\frac{1}{6}-\frac{1}{5}\right):\frac{17}{13}-\frac{20}{3}.\left(\frac{2}{5}-\frac{1}{4}\right)+\frac{2}{3}.\left(\frac{6}{5}-\frac{9}{2}\right)\)

\(=\frac{17}{13}:\left(-2\right).\frac{-1}{30}.\frac{13}{17}-\frac{20}{3}.\frac{3}{20}+\frac{2}{3}.\frac{-33}{10}\)

\(=\left(\frac{17}{13}.\frac{13}{17}\right).\left[\frac{-1}{30}:\left(-2\right)\right]-1+\frac{-11}{5}\)

\(=1.\frac{1}{60}-1-\frac{11}{5}\)\(=\frac{-191}{60}\)

a) 12⁸ . 9¹²

= ( 3 . 4 )⁸ . 9¹²

= 3⁸ . 4⁸

= ( 3² )⁴ . ( 2² )⁸

= 9⁴ . 2¹⁶ . 9¹²

= 2¹⁶ . 9¹⁶

= ( 2 . 9 )¹⁶ = 18¹⁶

b) 45¹⁰ . 5³⁰

= ( 5 . 9 )¹⁰ . 5³⁰

= 5¹⁰ . 9¹⁰ . 5³⁰

= 5⁴⁰ . ( 3² )¹⁰

= ( 5² )²⁰ . 3²⁰

= 25²⁰ . 3²⁰

= ( 25 . 3 )²⁰ = 75²⁰

\(\left(-3\right)^{20}=3^{20}=\left(3^2\right)^{10}=9^{10}\)

\(\left(-2\right)^{30}=2^{30}=\left(2^3\right)^{10}=8^{10}\)

Có \(9>8>0\Rightarrow9^{10}>8^{10}\)

Do đó \(\left(-3\right)^{20}>\left(-2\right)^{30}\). 

ta có :

\(\left(-3\right)^{20}=3^{20}>2^{20}=\left(-2\right)^{20}\)

nên ta có : \(\left(-3\right)^{20}>\left(-2\right)^{20}\)

\(\frac{8^5.\left(-5\right)^8+\left(-2\right)^5.10^9}{2^{16}.5^7+20^8}\)

\(=\frac{\left(2^3\right)^5.5^8+\left(-1\right)^5.2^5.\left(2.5\right)^9}{2^{16}.5^7+\left(2^2.5\right)^8}\)

\(=\frac{2^{15}.5^8+\left(-1\right).2^5.2^9.5^9}{2^{16}.5^7+\left(2^2\right)^8.5^8}\)

\(=\frac{2^{15}.5^8+\left(-1\right).2^{14}.5^9}{2^{16}.5^7+2^{16}.5^8}\)

\(=\frac{2^{14}.5^8.\left(2-1-5\right)}{2^{16}.5^7.\left(1+5\right)}\)

\(=\frac{5.\left(-4\right)}{2^2.6}=\frac{-20}{24}=\frac{-5}{6}\)

Mình nhầm xíu :

\(\frac{8^5.\left(-5\right)^8+\left(-2\right)^5.10^9}{2^{16}.5^7+20^8}=\frac{\left(2^3\right)^5.5^8+\left(-1\right)^5.2^5.\left(2.5\right)^9}{2^{16}.5^7+\left(2^2.5\right)^8}\)

\(=\frac{2^{15}.5^8+\left(-1\right).2^5.2^9.5^9}{2^{16}.5^7+\left(2^2\right)^8.5^8}\)\(=\frac{2^{15}.5^8+\left(-1\right).2^{14}.5^9}{2^{16}.5^7+2^{16}.5^8}\)

\(=\frac{2^{14}.5^8.\left(2-1.5\right)}{2^{16}.5^7.\left(1+5\right)}\)\(=\frac{5.\left(-3\right)}{2^2.6}=\frac{-15}{24}=\frac{-5}{8}\)