<span>(6,1*10^-2)(6*10^-4) = 36,6*10^-6</span>
1)
![\displaystyle \sqrt{6^4} = \sqrt{(6^2)^2}=6^2=36](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B6%5E4%7D%20%3D%20%5Csqrt%7B%286%5E2%29%5E2%7D%3D6%5E2%3D36%20)
2)
![\displaystyle \sqrt{(-5)^6}= \sqrt{(-1)^6*5^6}= \sqrt{1*(5^3)^2}=5^3=125](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-5%29%5E6%7D%3D%20%5Csqrt%7B%28-1%29%5E6%2A5%5E6%7D%3D%20%5Csqrt%7B1%2A%285%5E3%29%5E2%7D%3D5%5E3%3D125%20)
Заметим что Четная степень отрицательного числа = положительному числу
3)
![\displaystyle \sqrt{(-8)^4}= \sqrt{(-1)^4*8^4}=8^2=64](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-8%29%5E4%7D%3D%20%5Csqrt%7B%28-1%29%5E4%2A8%5E4%7D%3D8%5E2%3D64%20%20)
4)
![\displaystyle \sqrt{0.1^6}= \sqrt{(0.1^3)^2}=0.1^3= 0.001](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B0.1%5E6%7D%3D%20%5Csqrt%7B%280.1%5E3%29%5E2%7D%3D0.1%5E3%3D%200.001)
5)
![\displaystyle \sqrt{(-1)^{4n}}= \sqrt{((-1)^2)^{2n}} =\sqrt{1^{2n}}= 1^{2n}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-1%29%5E%7B4n%7D%7D%3D%20%5Csqrt%7B%28%28-1%29%5E2%29%5E%7B2n%7D%7D%20%3D%5Csqrt%7B1%5E%7B2n%7D%7D%3D%201%5E%7B2n%7D%3D1%20)
6)
![\displaystyle \sqrt{(-1)^{4n+6}}= \sqrt{((-1)^2)^{2n+3}}= \sqrt{1^{2n+3}}=1^{2n+3}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-1%29%5E%7B4n%2B6%7D%7D%3D%20%5Csqrt%7B%28%28-1%29%5E2%29%5E%7B2n%2B3%7D%7D%3D%20%5Csqrt%7B1%5E%7B2n%2B3%7D%7D%3D1%5E%7B2n%2B3%7D%3D1%20%20%20)
15-12а-12а+7= 22-24а= 22-12= 10
5у² + у + у³ + 5 = у²(5 + у) + (5 + у) = (у² + 1)(5 + у)
у³ - 4 + 2у - 2у² = у²(у - 2) + 2(у - 2) = (у² + 2)(у - 2)
7с² - с - с³ + 7 = с²(7 - с) + (7 - с) = (с² + 1)(7 - с)
х³ + 28 - 14х² - 2х = х(х² - 2) - 14(х² - 2) = (х - 14)(х² - 2)
16ab² + 5b²c + 10c³ + 32ac² = 16a(b² + 2c²) + 5c(b² + 2c²) = (16a + 5c)(b² + 2c²)
20n² - 35a - 14an + 50n = 10n(2n + 5) - 7a(2n + 5) = (10n - 7a)(2n + 5)
40a³bc + 21bc - 56ac² - 15a²b² = 5a²b(8ac - 3b) - 7c(8ac - 3b) = (5a²b - 7c)(8ac - 3b)
16xy² - 5y²z - 10z³ + 32xz² = 16x(y² + 2z²) - 5z(y² + 2z²) = (16x - 5z)(y² + 2z²)