1) (2⁸•7⁹)/( 14¹⁰)•(26⁵•2¹⁰)/( 13⁶•8⁴) 2) (12⁵)/(2³•4⁴) 3) (2⁸•7⁹)/(14¹⁰):(26⁵)/(13⁶•8⁴)...

Question 1

1) (2⁸•7⁹)/( 14¹⁰)•(26⁵•2¹⁰)/( 13⁶•8⁴)
2) (12⁵)/(2³•4⁴)
3) (2⁸•7⁹)/(14¹⁰):(26⁵)/(13⁶•8⁴)
4) (12⁵)/(2³•3⁴)•(10⁵)/(2⁶•5⁷)

Question 2

Решите задачу:

$1) \frac{2^8\cdot 7^9}{14^{10}} \cdot \frac{26^5\cdot 2^{10}}{13^6\cdot 8^4} =\frac{2^8\cdot 7^9}{(2\cdot7)^{10}} \cdot \frac{(2\cdot 13)^5\cdot 2^{10}}{13^6\cdot (2^3)^4} = \\ \\= \frac{1}{2^2\cdot7} \cdot \frac{2^5\cdot 13^5\cdot 2^{10}}{13^6\cdot 2^{12}} = \\ \\ = \frac{2^{5+10}\cdot 13^5}{2^{2+12}\cdot 13^6\cdot 7^{10}} = \frac{2}{7\cdot 13}=\frac{2}{91}$

$2) \frac{12^5}{2^3\cdot 4^4}= \frac{(3\cdot 4)^5}{2^3\cdot 4^4}= \frac{3^5\cdot 4^5}{2^3\cdot 4^4}= \frac{3^5\cdot 4}{8}= \frac{3^5}{2}= \frac{243}{2}$

$3) \frac{2^8\cdot 7^9}{14^{10}} : \frac{26^5}{13^6\cdot 8^4} =\frac{2^8\cdot 7^9}}{(2\cdot7)^{10}} : \frac{(2\cdot 13)^5}{13^6\cdot (2^3)^4} =\frac{2^8\cdot 7^9}{2^{10}\cdot7^{10}} :\frac{2^5\cdot 13^5}{13^6\cdot 2^{12}} = \\ \\ =\frac{1}{2^2\cdot7} \cdot\frac{13\cdot 2^7}{1} = \frac{2^{5}\cdot 13}{7}=\frac{416}{7}$

$4) \frac{12^5}{2^3\cdot 3^4}\cdot \frac{10^5}{2^6\cdot 5^7} = \frac{(3\cdot 4)^5}{2^3\cdot 3^4}\cdot \frac{(2\cdot 5)^5}{2^6\cdot 5^7} = \frac{3^5\cdot 4^5}{2^3\cdot 3^4}\cdot \frac{2^5\cdot 5^5}{2^6\cdot 5^7}= \frac{3\cdot 2^7}{2\cdot 5^2}= \frac{384}{50}= \frac{768}{100}= \\ \\ =7,68$