Представь данную степень в виде квадрата и вычисли.

Задание 2. а) $3^{28} = (3^{14})^2$ б) $5^{14} = (5^{7})^2$ в) $9^6 = (9^3)^2$ г) $2^{76} = (2^{38})^2$ д) $2^{-8} = (2^{-4})^2$ е) $2^{-16} = (2^{-8})^2$ Задание 3. 1) a) $\sqrt{2^8} = 2^4 = 16$ в) $\sqrt{5^4} = 5^2 = 25$ б) $\sqrt{3^6} = 3^3 = 27$ г) $\sqrt{3^4 \cdot 2^6} = \sqrt{3^4} \cdot \sqrt{2^6} = 3^2 \cdot 2^3 = 9 \cdot 8 = 72$ д) $\sqrt{2^8 \cdot 5^6} = \sqrt{2^8} \cdot \sqrt{5^6} = 2^4 \cdot 5^3 = 16 \cdot 125 = 2000$ е) $\sqrt{\frac{2^{10}}{3^2 \cdot 5^4}} = \frac{\sqrt{2^{10}}}{\sqrt{3^2 \cdot 5^4}} = \frac{2^5}{3 \cdot 5^2} = \frac{32}{3 \cdot 25} = \frac{32}{75}$ 2) a) $\sqrt{3^4} = 3^2 = 9$ б) $\sqrt{2^{10}} = 2^5 = 32$ в) $\sqrt{10^6} = 10^3 = 1000$ г) $\sqrt{3^6 \cdot 2^4} = \sqrt{3^6} \cdot \sqrt{2^4} = 3^3 \cdot 2^2 = 27 \cdot 4 = 108$ д) $\sqrt{5^4 \cdot 2^8} = \sqrt{5^4} \cdot \sqrt{2^8} = 5^2 \cdot 2^4 = 25 \cdot 16 = 400$ е) $\sqrt{\frac{2^{10}}{3^4 \cdot 5^2}} = \frac{\sqrt{2^{10}}}{\sqrt{3^4 \cdot 5^2}} = \frac{2^5}{3^2 \cdot 5} = \frac{32}{9 \cdot 5} = \frac{32}{45}$ 3) a) $\sqrt{2,5 \cdot 10} = \sqrt{25} = 5$ б) $\sqrt{50 \cdot 98} = \sqrt{2 \cdot 25 \cdot 2 \cdot 49} = \sqrt{2^2 \cdot 5^2 \cdot 7^2} = 2 \cdot 5 \cdot 7 = 70$ в) $\sqrt{0,08 \cdot 4,5} = \sqrt{\frac{8}{100} \cdot \frac{45}{10}} = \sqrt{\frac{2^3 \cdot 3^2 \cdot 5}{10^3}} = \sqrt{\frac{2^3 \cdot 3^2 \cdot 5}{2^3 \cdot 5^3}} = \sqrt{\frac{3^2}{5^2}} = \frac{3}{5} = 0,6$ г) $\sqrt{75 \cdot 27} = \sqrt{3 \cdot 25 \cdot 3^3} = \sqrt{3^4 \cdot 5^2} = 3^2 \cdot 5 = 9 \cdot 5 = 45$ 4) a) $\sqrt{10 \cdot 3,6} = \sqrt{36} = 6$ б) $\sqrt{8 \cdot 98} = \sqrt{2^3 \cdot 2 \cdot 49} = \sqrt{2^4 \cdot 7^2} = 2^2 \cdot 7 = 4 \cdot 7 = 28$ в) $\sqrt{0,18 \cdot 2} = \sqrt{\frac{18}{100} \cdot 2} = \sqrt{\frac{36}{100}} = \frac{6}{10} = 0,6$ г) $\sqrt{12 \cdot 27} = \sqrt{4 \cdot 3 \cdot 9 \cdot 3} = \sqrt{2^2 \cdot 3^2 \cdot 3^2} = 2 \cdot 3 \cdot 3 = 18$