1 Evaluate without using a calculator: \( 11 \sqrt[4]{10000} \) \( 1.2 \sqrt[3]{64^{2}} \) \( 13 \sqrt[4]{16^{3}} \) \( 1.4(0,125)^{-\frac{2}{3}} \) \( 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} \) \( 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} \) \( 1.7 \quad(-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} \) \( 1.8(0,0625)^{-\frac{1}{4}} \) \( 7.9(0,064)^{\frac{2}{3}} \) \( 1.10 \quad 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) \) \( 1.1149^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) \) \( 1.1216^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{-\frac{1}{3}} \)

Calculate the value by following steps: - step0: Calculate: \(11\times 10000^{\frac{1}{4}}\) - step1: Evaluate the power: \(11\times 10\) - step2: Multiply: \(110\) Calculate or simplify the expression \( (-2)^0 + (8)^(1/3) + (3)^(2) \). Calculate the value by following steps: - step0: Calculate: \(\left(-2\right)^{0}+8^{\frac{1}{3}}+3^{2}\) - step1: Evaluate the power: \(1+8^{\frac{1}{3}}+3^{2}\) - step2: Evaluate the power: \(1+2+3^{2}\) - step3: Evaluate the power: \(1+2+9\) - step4: Add the numbers: \(12\) Calculate or simplify the expression \( 13 * (16^3)^(1/4) \). Calculate the value by following steps: - step0: Calculate: \(13\left(16^{3}\right)^{\frac{1}{4}}\) - step1: Multiply the exponents: \(13\times 16^{3\times \frac{1}{4}}\) - step2: Multiply: \(13\times 16^{\frac{3}{4}}\) - step3: Evaluate the power: \(13\times 8\) - step4: Multiply: \(104\) Calculate or simplify the expression \( (0.0625)^(-1/4) \). Calculate the value by following steps: - step0: Calculate: \(0.0625^{\frac{-1}{4}}\) - step1: Rewrite the fraction: \(0.0625^{-\frac{1}{4}}\) - step2: Convert the expressions: \(\left(\frac{1}{16}\right)^{-\frac{1}{4}}\) - step3: Transform the expression: \(16^{\frac{1}{4}}\) - step4: Factor the number: \(\left(2^{4}\right)^{\frac{1}{4}}\) - step5: Evaluate the power: \(2\) Calculate or simplify the expression \( 1.2 * (64^2)^(1/3) \). Calculate the value by following steps: - step0: Calculate: \(1.2\left(64^{2}\right)^{\frac{1}{3}}\) - step1: Multiply the exponents: \(1.2\times 64^{2\times \frac{1}{3}}\) - step2: Multiply: \(1.2\times 64^{\frac{2}{3}}\) - step3: Rewrite the expression: \(1.2\times 16\) - step4: Multiply the numbers: \(19.2\) Calculate or simplify the expression \( 7.9 * (0.064)^(2/3) \). Calculate the value by following steps: - step0: Calculate: \(7.9\times 0.064^{\frac{2}{3}}\) - step1: Convert the expressions: \(7.9\left(\frac{8}{125}\right)^{\frac{2}{3}}\) - step2: Convert the expressions: \(\frac{79}{10}\left(\frac{8}{125}\right)^{\frac{2}{3}}\) - step3: Multiply the numbers: \(\frac{158}{125}\) Calculate or simplify the expression \( 1.4 * (0.125)^(-2/3) \). Calculate the value by following steps: - step0: Calculate: \(1.4\times 0.125^{\frac{-2}{3}}\) - step1: Rewrite the fraction: \(1.4\times 0.125^{-\frac{2}{3}}\) - step2: Convert the expressions: \(1.4\left(\frac{1}{8}\right)^{-\frac{2}{3}}\) - step3: Rewrite the expression: \(1.4\times 4\) - step4: Multiply the numbers: \(5.6\) Calculate or simplify the expression \( 81^(-3/4) * (27^(2/3) - 9^(3/2)) \). Calculate the value by following steps: - step0: Calculate: \(81^{\frac{-3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right)\) - step1: Subtract the numbers: \(81^{\frac{-3}{4}}\left(-18\right)\) - step2: Rewrite the fraction: \(81^{-\frac{3}{4}}\left(-18\right)\) - step3: Evaluate the power: \(\frac{1}{27}\left(-18\right)\) - step4: Multiply: \(-\frac{2}{3}\) Calculate or simplify the expression \( 49^(-1/2) * (125^(2/3) - 9^0) \). Calculate the value by following steps: - step0: Calculate: \(49^{\frac{-1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right)\) - step1: Evaluate the power: \(49^{\frac{-1}{2}}\left(125^{\frac{2}{3}}-1\right)\) - step2: Subtract the numbers: \(49^{\frac{-1}{2}}\times 24\) - step3: Rewrite the fraction: \(49^{-\frac{1}{2}}\times 24\) - step4: Evaluate the power: \(\frac{1}{7}\times 24\) - step5: Multiply: \(\frac{24}{7}\) Calculate or simplify the expression \( 1.6 * (1 + 11/25)^(-1/2) \). Calculate the value by following steps: - step0: Calculate: \(1.6\left(1+\frac{11}{25}\right)^{\frac{-1}{2}}\) - step1: Add the numbers: \(1.6\left(\frac{36}{25}\right)^{\frac{-1}{2}}\) - step2: Rewrite the fraction: \(1.6\left(\frac{36}{25}\right)^{-\frac{1}{2}}\) - step3: Convert the expressions: \(\frac{8}{5}\left(\frac{36}{25}\right)^{-\frac{1}{2}}\) - step4: Multiply the numbers: \(\frac{4}{3}\) Calculate or simplify the expression \( 16^(1/2) + 16^(3/4) - 64^(-1/3) \). Calculate the value by following steps: - step0: Calculate: \(16^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{\frac{-1}{3}}\) - step1: Rewrite the fraction: \(16^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{-\frac{1}{3}}\) - step2: Evaluate the power: \(4+16^{\frac{3}{4}}-64^{-\frac{1}{3}}\) - step3: Evaluate the power: \(4+8-64^{-\frac{1}{3}}\) - step4: Evaluate the power: \(4+8-\frac{1}{4}\) - step5: Add the numbers: \(12-\frac{1}{4}\) - step6: Reduce fractions to a common denominator: \(\frac{12\times 4}{4}-\frac{1}{4}\) - step7: Transform the expression: \(\frac{12\times 4-1}{4}\) - step8: Multiply the numbers: \(\frac{48-1}{4}\) - step9: Subtract the numbers: \(\frac{47}{4}\) Calculate or simplify the expression \( 1.5 * (2 + 14/25)^(-1/2) \). Calculate the value by following steps: - step0: Calculate: \(1.5\left(2+\frac{14}{25}\right)^{\frac{-1}{2}}\) - step1: Add the numbers: \(1.5\left(\frac{64}{25}\right)^{\frac{-1}{2}}\) - step2: Rewrite the fraction: \(1.5\left(\frac{64}{25}\right)^{-\frac{1}{2}}\) - step3: Convert the expressions: \(\frac{3}{2}\left(\frac{64}{25}\right)^{-\frac{1}{2}}\) - step4: Multiply the numbers: \(\frac{15}{16}\) Let's evaluate each expression step by step: 1. **Evaluate \( 11 \sqrt[4]{10000} \)**: - First, calculate \( \sqrt[4]{10000} \): \[ \sqrt[4]{10000} = (10000)^{1/4} = (10^4)^{1/4} = 10 \] - Now, multiply by 11: \[ 11 \times 10 = 110 \] 2. **Evaluate \( 1.2 \sqrt[3]{64^{2}} \)**: - Calculate \( \sqrt[3]{64^2} \): \[ \sqrt[3]{64^2} = (64)^{2/3} = (4^3)^{2/3} = 4^2 = 16 \] - Now, multiply by 1.2: \[ 1.2 \times 16 = 19.2 \] 3. **Evaluate \( 13 \sqrt[4]{16^{3}} \)**: - Calculate \( \sqrt[4]{16^3} \): \[ \sqrt[4]{16^3} = (16)^{3/4} = (4^2)^{3/4} = 4^{3/2} = 8 \] - Now, multiply by 13: \[ 13 \times 8 = 104 \] 4. **Evaluate \( 1.4(0.125)^{-\frac{2}{3}} \)**: - Calculate \( (0.125)^{-\frac{2}{3}} \): \[ (0.125)^{-\frac{2}{3}} = (1/8)^{-\frac{2}{3}} = 8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^2 = 4 \] - Now, multiply by 1.4: \[ 1.4 \times 4 = 5.6 \] 5. **Evaluate \( 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} \)**: - Convert \( 2 \frac{14}{25} \) to an improper fraction: \[ 2 \frac{14}{25} = \frac{50 + 14}{25} = \frac{64}{25} \] - Calculate \( \left(\frac{64}{25}\right)^{-\frac{1}{2}} \): \[ \left(\frac{64}{25}\right)^{-\frac{1}{2}} = \frac{25^{1/2}}{64^{1/2}} = \frac{5}{8} \] - Now, multiply by 1.5: \[ 1.5 \times \frac{5}{8} = \frac{7.5}{8} = \frac{15}{16} \] 6. **Evaluate \( 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} \)**: - Convert \( 1 \frac{11}{25} \) to an improper fraction: \[ 1 \frac{11}{25} = \frac{25 + 11}{25} = \frac{36}{25} \] - Calculate \( \left(\frac{36}{25}\right)^{-\frac{1}{2}} \): \[ \left(\frac{36}{25}\right)^{-\frac{1}{2}} = \frac{25^{1/2}}{36^{1/2}} = \frac{5}{6} \] - Now, multiply by 1.6: \[ 1.6 \times \frac{5}{6} = \frac{8}{3} = 2\frac{2}{3} \] 7. **Evaluate \( (-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} \)**: - Calculate each term: \[ (-2)^{0} = 1, \quad \sqrt[3]{8} = 2, \quad \left(\sqrt{3}\right)^{2} = 3 \] - Now, sum them: \[ 1 + 2 + 3 = 6 \] 8. **Evaluate \( (0.0625)^{-\frac{1}{4}} \)**: - Calculate \( (0.0625)^{-\frac{1}{4}} \): \[ (0.0625)^{-\frac{1}{4}} = (1/16)^{-\frac{1}{4}} = 16^{\frac{1}{4}} = 2 \] 9. **Evaluate \( 7.9(0.064)^{\frac{2}{3}} \)**: - Calculate \( (0.064)^{\frac{2}{3}} \): \[ (0.064)^{\frac{2}{3}} = (1/16)^{\frac{2}{3}} = 16^{-\frac{2}{3}} = \frac{1}{4} \] - Now, multiply by 7.9: \[ 7.9 \times \frac{1}{4} = 1.975 \] 10. **Evaluate \( 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) \)**: - Calculate each part: \[ 81^{-\frac{3}{4}} = (3^4)^{-\frac{3}{4}} = 3^{-3} = \frac{1}{27} \] \[ 27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}} = 3^2 = 9 \] \[ 9^{\frac{3}{2}} = (3^2)^{\frac{3}{2}} = 3^3 = 27 \] - Now, calculate the expression: \[ 9 - 27 = -18 \] \[ \frac{1}{27} \times (-18) = -\frac{2}{3} \] 11. **Evaluate \( 49^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) \)**: