Упр.20.10 ГДЗ Мордкович Семенов 8 класс (Алгебра)

а) (1/v3)^(-4) + (1/2)^(-3) · 3^3;
б) (v2/3)^(-6) · 3^(-2) + (3/v2)^(-4);
в) (5/6)^2 · (v5/3)^(-4) — (v2)^(-4);
г) (v8)^(-4) + (5/v2)^(-2) · (1/5)^(-5);
д) (6/5)^(-2) · (v6)^6 — (1/v5)^(-4);
е) (v3/2)^(-2) : 1,5^(-4) — (2/v3)^(-4).

1. а)

   $$\left(\frac{1}{\sqrt{3}}\right)^{-4}+\left(\frac{1}{2}\right)^{-3}\cdot 3^3 =(\sqrt{3})^4+2^3\cdot 3^3 =9+8\cdot 27 =9+216=225.$$

2. б)

   $$\left(\frac{\sqrt{2}}{3}\right)^{-6}\cdot 3^{-2}+\left(\frac{3}{\sqrt{2}}\right)^{-4} =\left(\frac{3}{\sqrt{2}}\right)^6\cdot \frac{1}{3^2}+\left(\frac{\sqrt{2}}{3}\right)^4$$
   $$=\frac{3^6}{(\sqrt{2})^6\cdot 3^2}+\frac{(\sqrt{2})^4}{3^4} =\frac{3^4}{(\sqrt{2})^6}+\frac{4}{81} =\frac{81}{8}+\frac{4}{81} =\frac{6561+32}{648} =\frac{6593}{648} =10\frac{113}{648}.$$

3. в)

   $$\left(\frac{5}{6}\right)^2\cdot \left(\frac{\sqrt{5}}{3}\right)^{-4}-\left(\sqrt{2}\right)^{-4} =\frac{25}{36}\cdot \left(\frac{3}{\sqrt{5}}\right)^4-\frac{1}{(\sqrt{2})^4}$$
   $$=\frac{25}{36}\cdot \frac{81}{25}-\frac{1}{4} =\frac{81}{36}-\frac{1}{4} =\frac{9}{4}-\frac{1}{4} =2.$$

4. г)

   $$\left(\sqrt{8}\right)^{-4}+\left(\frac{5}{\sqrt{2}}\right)^{-2}\cdot \left(\frac{1}{5}\right)^{-5} =\frac{1}{(\sqrt{8})^4}+\left(\frac{\sqrt{2}}{5}\right)^2\cdot 5^5$$
   $$=\frac{1}{8^2}+\frac{2}{25}\cdot 5^5 =\frac{1}{64}+\frac{2}{25}\cdot 3125 =\frac{1}{64}+250 =250\frac{1}{64}.$$

5. д)

   $$\left(\frac{6}{5}\right)^{-2}\cdot (\sqrt{6})^6-\left(\frac{1}{\sqrt{5}}\right)^{-4} =\left(\frac{5}{6}\right)^2\cdot \left((\sqrt{6})^2\right)^3-(\sqrt{5})^4$$
   $$=\frac{25}{36}\cdot 6^3-25 =\frac{25}{36}\cdot 216-25 =25\cdot 6-25 =25\cdot 5 =125.$$

6. е)

   $$\left(\frac{\sqrt{3}}{2}\right)^{-2}:1{,}5^{-4}-\left(\frac{2}{\sqrt{3}}\right)^{-4} =\left(\frac{2}{\sqrt{3}}\right)^2:\left(\frac{3}{2}\right)^{-4}-\left(\frac{\sqrt{3}}{2}\right)^4$$
   $$=\frac{4}{3}:\frac{16}{81}-\frac{9}{16} =\frac{4}{3}\cdot \frac{81}{16}-\frac{9}{16} =\frac{108}{16}-\frac{9}{16} =\frac{99}{16} =6\frac{3}{16}.$$

Ответ

а) 225; б) $$\frac{6593}{648}$$; в) 2; г) $$250\frac{1}{64}$$; д) 125; е) $$6\frac{3}{16}$$.