Viết lại 64 ở dạng 82 .

64² =4096

1 phần 5

\(1.\left(5\right)\)

\(=\frac{14}{9}\)

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

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

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

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

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

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