1 Evaluate without using a calculator: \( 11 \sqrt[4]{10000} \) \( 1.2 \sqrt[3]{64^{2}} \) \( 13 \sqrt[4]{16^{3}} \) \( 1.4(0,125)^{-\frac{2}{3}} \) \( 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} \) \( 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} \) \( 1.7 \quad(-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} \) \( 1.8(0,0625)^{-\frac{1}{4}} \) \( 7.9(0,064)^{\frac{2}{3}} \) \( 1.10 \quad 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) \) \( 1.1149^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) \) \( 1.1216^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{-\frac{1}{3}} \)
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To tackle the evaluations, let's break down the expressions one by one: ### Step 1: Evaluate each expression 1. **\(11 \sqrt[4]{10000}\)** \(\sqrt[4]{10000} = \sqrt[4]{10^4} = 10\) So, \(11 \cdot 10 = 110\) 2. **\(1.2 \sqrt[3]{64^{2}}\)** We know \(64 = 4^3\), thus \(64^2 = (4^3)^2 = 4^6\) and \(\sqrt[3]{4^6} = 4^2 = 16\) Therefore, \(1.2 \cdot 16 = 19.2\) 3. **\(13 \sqrt[4]{16^{3}}\)** \(16 = 2^4\) → \(16^3 = (2^4)^3 = 2^{12}\) \(\sqrt[4]{2^{12}} = 2^{3} = 8\) So, \(13 \cdot 8 = 104\) 4. **\(1.4(0.125)^{-\frac{2}{3}}\)** \(0.125 = \frac{1}{8} = 2^{-3}\) Thus, \((0.125)^{-\frac{2}{3}} = (2^{-3})^{-\frac{2}{3}} = 2^2 = 4\) So, \(1.4 \cdot 4 = 5.6\) 5. **\(1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}}\)** \(2 \frac{14}{25} = \frac{64}{25}\) \(\left(\frac{64}{25}\right)^{-\frac{1}{2}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8}\) Therefore, \(1.5 \cdot \frac{5}{8} = \frac{7.5}{8} = 0.9375\) 6. **\(1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}}\)** \(1 \frac{11}{25} = \frac{36}{25}\) \(\left(\frac{36}{25}\right)^{-\frac{1}{2}} = \frac{\sqrt{25}}{\sqrt{36}} = \frac{5}{6}\) So, \(1.6 \cdot \frac{5}{6} = \frac{8}{6} = \frac{4}{3} = 1.3333\) 7. **\((-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2}\)** \((-2)^0 = 1\), \(\sqrt[3]{8} = 2\), \((\sqrt{3})^2 = 3\) Therefore, \(1 + 2 + 3 = 6\) 8. **\( (0.0625)^{-\frac{1}{4}}\)** \(0.0625 = \frac{1}{16} = 4^{-2}\) Thus, \((0.0625)^{-\frac{1}{4}} = (4^{-2})^{-\frac{1}{4}} = 4^{\frac{1}{2}} = 2\) 9. **\(7.9(0.064)^{\frac{2}{3}}\)** \(0.064 = \frac{1}{16} = 4^{-2}\) Thus, \((0.064)^{\frac{2}{3}} = \left(4^{-2}\right)^{\frac{2}{3}} = 4^{-\frac{4}{3}} = \frac{1}{8}\) So, \(7.9 \cdot \frac{1}{8} = 0.9875\) 10. **\( 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right)\)** \(81^{-\frac{3}{4}} = (3^4)^{-\frac{3}{4}} = 3^{-3} = \frac{1}{27}\),