Задание 36. Выполните возведение в степень: 1) $$(b^2)^3 = b^{2\cdot 3} = b^6$$ 2) $$(a^5)^{10} =$$ 3) $$(c^4)^{12} =$$ 4) $$(k^5)^5 =$$ 5) $$(p^4)^5 =$$ 13) $$(k^{13})^3 =$$ 14) $$(a^{11})^5 =$$ 15) $$(k^{3n})^2 =$$ Представьте степень в виде произведения степеней: 16) $$(ab)^5 = a^5 \cdot b^5$$ 17) $$(xy)^3 = x^3 \cdot y^3$$ 18) $$(an)^2 = a^2 \cdot n^2$$ 19) $$(2a)^5 = 2^5 \cdot a^5$$ 20) $$(5c)^2 = 5^2 \cdot c^2$$ 28) $$(9m^2)^2 = 9^2 \cdot m^4$$ 29) $$(-5n^3)^2 = (-5)^2 \cdot (n^3)^2 = 25 \cdot n^6$$ 30) $$(-2a^6)^3 = (-2)^3 \cdot (a^6)^3 = -8a^{18}$$ Найдите значение выражения: 31) $$2^5 \cdot 5^5 = (2 \cdot 5)^5 = 10^5 = 100000$$ 32) $$14^6 \cdot (\frac{1}{7})^6 =$$ 33) $$0,25^9 \cdot 4^9 =$$ 34) $$(2^2)^3 : 2^3 =$$ 35) $$\frac{(2^{10})^2 : 2^7}{2^7} =$$ 43) $$\frac{(2^2)^9 \cdot 8}{2^{20}} =$$ 44) $$\frac{27 \cdot (3^4)^6}{3^{29} \cdot 3^5} =$$ 45) $$\frac{5^{15} \cdot 5^{12}}{125 \cdot (5^8)^3} =$$ 24) $$10000 : 10^4 \cdot 10^0 =$$ 25) $$5^{10} : 625 : 25 =$$ 26) $$0,25 \cdot (\frac{1}{4})^2 =$$ 0) $$(\frac{1}{2})^8 : (\frac{1}{2})^7 : (\frac{1}{2})^4 : (\frac{1}{2})^6 =$$ 1) $$(\frac{1}{3})^7 : (\frac{1}{3})^5 \cdot \frac{1}{3} = $$

Ответ:

1. $$(a^5)^{10} = a^{5 \cdot 10} = \mathbf{a^{50}}$$
2. $$(c^4)^{12} = c^{4 \cdot 12} = \mathbf{c^{48}}$$
3. $$(k^5)^5 = k^{5 \cdot 5} = \mathbf{k^{25}}$$
4. $$(p^4)^5 = p^{4 \cdot 5} = \mathbf{p^{20}}$$
5. $$(k^{13})^3 = k^{13 \cdot 3} = \mathbf{k^{39}}$$
6. $$(a^{11})^5 = a^{11 \cdot 5} = \mathbf{a^{55}}$$
7. $$(k^{3n})^2 = k^{3n \cdot 2} = \mathbf{k^{6n}}$$
8. $$14^6 \cdot (\frac{1}{7})^6 = (14 \cdot \frac{1}{7})^6 = 2^6 = \mathbf{64}$$
9. $$0,25^9 \cdot 4^9 = (0,25 \cdot 4)^9 = 1^9 = \mathbf{1}$$
10. $$(2^2)^3 : 2^3 = 2^{2 \cdot 3} : 2^3 = 2^6 : 2^3 = 2^{6-3} = 2^3 = \mathbf{8}$$
11. $$\frac{(2^{10})^2 : 2^7}{2^7} = \frac{2^{20} : 2^7}{2^7} = \frac{2^{20-7}}{2^7} = \frac{2^{13}}{2^7} = 2^{13-7} = 2^6 = \mathbf{64}$$
12. $$\frac{(2^2)^9 \cdot 8}{2^{20}} = \frac{2^{18} \cdot 2^3}{2^{20}} = \frac{2^{21}}{2^{20}} = 2^{21-20} = 2^1 = \mathbf{2}$$
13. $$\frac{27 \cdot (3^4)^6}{3^{29} \cdot 3^5} = \frac{3^3 \cdot 3^{24}}{3^{34}} = \frac{3^{27}}{3^{34}} = 3^{27-34} = 3^{-7} = \frac{1}{3^7} = \frac{1}{2187} = \mathbf{\frac{1}{2187}}$$
14. $$\frac{5^{15} \cdot 5^{12}}{125 \cdot (5^8)^3} = \frac{5^{27}}{5^3 \cdot 5^{24}} = \frac{5^{27}}{5^{27}} = \mathbf{1}$$
15. $$10000 : 10^4 \cdot 10^0 = 10^4 : 10^4 \cdot 1 = 1 \cdot 1 = \mathbf{1}$$
16. $$5^{10} : 625 : 25 = 5^{10} : 5^4 : 5^2 = 5^{10-4-2} = 5^4 = \mathbf{625}$$
17. $$0,25 \cdot (\frac{1}{4})^2 = \frac{1}{4} \cdot (\frac{1}{4})^2 = (\frac{1}{4})^1 \cdot (\frac{1}{4})^2 = (\frac{1}{4})^{1+2} = (\frac{1}{4})^3 = \frac{1}{4^3} = \frac{1}{64} = \mathbf{\frac{1}{64}}$$
18. $$(\frac{1}{2})^8 : (\frac{1}{2})^7 : (\frac{1}{2})^4 : (\frac{1}{2})^6 = (\frac{1}{2})^{8-7-4-6} = (\frac{1}{2})^{-9} = 2^9 = \mathbf{512}$$
19. $$(\frac{1}{3})^7 : (\frac{1}{3})^5 \cdot \frac{1}{3} = (\frac{1}{3})^{7-5+1} = (\frac{1}{3})^3 = \frac{1}{3^3} = \mathbf{\frac{1}{27}}$$