Ответ:
1. в)
2. a)
б)
3. б)
в)
4.
5. а)
Объяснение:
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Answers & Comments
Ответ:
1. в)![(a^2)^4 = a^{2*4} = a^8 (a^2)^4 = a^{2*4} = a^8](https://tex.z-dn.net/?f=%28a%5E2%29%5E4%20%3D%20a%5E%7B2%2A4%7D%20%3D%20a%5E8)
2. a)![\frac{a^2*(a^4)^5}{a^5} = \frac{a^2*a^{24}}{a^5} = \frac{a^{26}}{a^5} = a^{21} \frac{a^2*(a^4)^5}{a^5} = \frac{a^2*a^{24}}{a^5} = \frac{a^{26}}{a^5} = a^{21}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E2%2A%28a%5E4%29%5E5%7D%7Ba%5E5%7D%20%3D%20%5Cfrac%7Ba%5E2%2Aa%5E%7B24%7D%7D%7Ba%5E5%7D%20%3D%20%5Cfrac%7Ba%5E%7B26%7D%7D%7Ba%5E5%7D%20%3D%20a%5E%7B21%7D)
б)![\frac{2^4*(2^3)^6}{2^3} = \frac{2^4*2^{18}}{2^3} = \frac{2^{22}}{2^3} = 2^{19} \frac{2^4*(2^3)^6}{2^3} = \frac{2^4*2^{18}}{2^3} = \frac{2^{22}}{2^3} = 2^{19}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E4%2A%282%5E3%29%5E6%7D%7B2%5E3%7D%20%3D%20%5Cfrac%7B2%5E4%2A2%5E%7B18%7D%7D%7B2%5E3%7D%20%3D%20%5Cfrac%7B2%5E%7B22%7D%7D%7B2%5E3%7D%20%3D%202%5E%7B19%7D)
3. б)![\frac{2^5*2^3}{4^3} = \frac{2^8}{2^6} = 2^2 = 4 \frac{2^5*2^3}{4^3} = \frac{2^8}{2^6} = 2^2 = 4](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E5%2A2%5E3%7D%7B4%5E3%7D%20%3D%20%5Cfrac%7B2%5E8%7D%7B2%5E6%7D%20%3D%202%5E2%20%3D%204)
в)![\frac{5^4*125}{25^4} = \frac{5^4*5^3}{5^8} = \frac{5^3}{5^4} = \frac{1}{5} = 0,2 \frac{5^4*125}{25^4} = \frac{5^4*5^3}{5^8} = \frac{5^3}{5^4} = \frac{1}{5} = 0,2](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E4%2A125%7D%7B25%5E4%7D%20%3D%20%5Cfrac%7B5%5E4%2A5%5E3%7D%7B5%5E8%7D%20%3D%20%5Cfrac%7B5%5E3%7D%7B5%5E4%7D%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%20%3D%200%2C2)
4.![(((2a)^2)^3)^4 = ((2a)^6)^4 = (2a)^{24} = 2^{24}a^{24} (((2a)^2)^3)^4 = ((2a)^6)^4 = (2a)^{24} = 2^{24}a^{24}](https://tex.z-dn.net/?f=%28%28%282a%29%5E2%29%5E3%29%5E4%20%3D%20%28%282a%29%5E6%29%5E4%20%3D%20%282a%29%5E%7B24%7D%20%3D%202%5E%7B24%7Da%5E%7B24%7D)
5. а)![(-0,2)^0 - 0,2^3 = 1-(\frac{1}{5})^3 = 1 - \frac{1}{125} = \frac{124}{125} (-0,2)^0 - 0,2^3 = 1-(\frac{1}{5})^3 = 1 - \frac{1}{125} = \frac{124}{125}](https://tex.z-dn.net/?f=%28-0%2C2%29%5E0%20-%200%2C2%5E3%20%3D%201-%28%5Cfrac%7B1%7D%7B5%7D%29%5E3%20%3D%201%20-%20%5Cfrac%7B1%7D%7B125%7D%20%3D%20%5Cfrac%7B124%7D%7B125%7D)
б)![\frac{8^3*128}{64} = 8^3*2 = 2^9*2 = 2^{10} = 1024 \frac{8^3*128}{64} = 8^3*2 = 2^9*2 = 2^{10} = 1024](https://tex.z-dn.net/?f=%5Cfrac%7B8%5E3%2A128%7D%7B64%7D%20%3D%208%5E3%2A2%20%3D%202%5E9%2A2%20%3D%202%5E%7B10%7D%20%3D%201024)
в)![\frac{15^12}{3^{12}*5^{10}} = \frac{5^{12}*3^{12}}{3^{12}*5^{10}} =5^2=25 \frac{15^12}{3^{12}*5^{10}} = \frac{5^{12}*3^{12}}{3^{12}*5^{10}} =5^2=25](https://tex.z-dn.net/?f=%5Cfrac%7B15%5E12%7D%7B3%5E%7B12%7D%2A5%5E%7B10%7D%7D%20%3D%20%5Cfrac%7B5%5E%7B12%7D%2A3%5E%7B12%7D%7D%7B3%5E%7B12%7D%2A5%5E%7B10%7D%7D%20%3D5%5E2%3D25)
Объяснение: