1. Write down the squares of these numbers. a) 11 b) 30 c) 0,5 d) 12 e) 80 f) 100 g) \( \frac{2}{5} \) h) \( \frac{3}{7} \) 2. Write down the cubes of these numbers. a) 10 b) 0,2 c) 5 d) 40 e) \( \frac{1}{2} \) f) \( \frac{2}{3} \) 3. Find the value of these numbers. a) square of 9 b) square root of 9 c) square of 4 d) square root of 4 e) cube of \( 1^{-} \) t) cubtervotufg 4. Without using a calculator, find the value of these numbers. a) \( \sqrt{400} \) b) \( \sqrt{0,01} \) c) \( \sqrt{0,36} \) d) \( \sqrt[3]{0,008} \) e) \( \sqrt[3]{\frac{1}{27}} \) f) \( \sqrt[3]{1000000} \) 5. Calculate. a) \( 2^{3} \times 3^{2} \) b) \( \sqrt{16} \times \sqrt{16} \) c) \( 2^{3} \times 2^{3} \) d) \( \sqrt{25} \times \sqrt{25} \)

Calculate the value by following steps: - step0: Calculate: \(12^{2}\) - step1: Evaluate the power: \(144\) Calculate or simplify the expression \( 30^2 \). Calculate the value by following steps: - step0: Calculate: \(30^{2}\) - step1: Evaluate the power: \(900\) Calculate or simplify the expression \( \sqrt(25) * \sqrt(25) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{25}\times \sqrt{25}\) - step1: Use the properties of radicals: \(\sqrt{25\times 25}\) - step2: Multiply the numbers: \(\sqrt{625}\) - step3: Write in exponential form: \(\sqrt{25^{2}}\) - step4: Simplify the root: \(25\) Calculate or simplify the expression \( 0.5^2 \). Calculate the value by following steps: - step0: Calculate: \(0.5^{2}\) - step1: Convert the expressions: \(\left(\frac{1}{2}\right)^{2}\) - step2: Use the properties of exponents: \(\frac{1^{2}}{2^{2}}\) - step3: Evaluate the power: \(\frac{1}{2^{2}}\) - step4: Evaluate the power: \(\frac{1}{4}\) Calculate or simplify the expression \( 11^2 \). Calculate the value by following steps: - step0: Calculate: \(11^{2}\) - step1: Evaluate the power: \(121\) Calculate or simplify the expression \( \sqrt(9) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{9}\) - step1: Write in exponential form: \(\sqrt{3^{2}}\) - step2: Simplify the root: \(3\) Calculate or simplify the expression \( 80^2 \). Calculate the value by following steps: - step0: Calculate: \(80^{2}\) - step1: Evaluate the power: \(6400\) Calculate or simplify the expression \( 100^2 \). Calculate the value by following steps: - step0: Calculate: \(100^{2}\) - step1: Evaluate the power: \(10000\) Calculate or simplify the expression \( (2/5)^2 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{2}{5}\right)^{2}\) - step1: Use the properties of exponents: \(\frac{2^{2}}{5^{2}}\) - step2: Evaluate the power: \(\frac{4}{5^{2}}\) - step3: Evaluate the power: \(\frac{4}{25}\) Calculate or simplify the expression \( 10^3 \). Calculate the value by following steps: - step0: Calculate: \(10^{3}\) - step1: Evaluate the power: \(1000\) Calculate or simplify the expression \( (3/7)^2 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{3}{7}\right)^{2}\) - step1: Use the properties of exponents: \(\frac{3^{2}}{7^{2}}\) - step2: Evaluate the power: \(\frac{9}{7^{2}}\) - step3: Evaluate the power: \(\frac{9}{49}\) Calculate or simplify the expression \( 0.2^3 \). Calculate the value by following steps: - step0: Calculate: \(0.2^{3}\) - step1: Convert the expressions: \(\left(\frac{1}{5}\right)^{3}\) - step2: Use the properties of exponents: \(\frac{1^{3}}{5^{3}}\) - step3: Evaluate the power: \(\frac{1}{5^{3}}\) - step4: Evaluate the power: \(\frac{1}{125}\) Calculate or simplify the expression \( 5^3 \). Calculate the value by following steps: - step0: Calculate: \(5^{3}\) - step1: Evaluate the power: \(125\) Calculate or simplify the expression \( 40^3 \). Calculate the value by following steps: - step0: Calculate: \(40^{3}\) - step1: Evaluate the power: \(64000\) Calculate or simplify the expression \( (1/2)^3 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{1}{2}\right)^{3}\) - step1: Use the properties of exponents: \(\frac{1^{3}}{2^{3}}\) - step2: Evaluate the power: \(\frac{1}{2^{3}}\) - step3: Evaluate the power: \(\frac{1}{8}\) Calculate or simplify the expression \( (2/3)^3 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{2}{3}\right)^{3}\) - step1: Use the properties of exponents: \(\frac{2^{3}}{3^{3}}\) - step2: Evaluate the power: \(\frac{8}{3^{3}}\) - step3: Evaluate the power: \(\frac{8}{27}\) Calculate or simplify the expression \( 9^2 \). Calculate the value by following steps: - step0: Calculate: \(9^{2}\) - step1: Evaluate the power: \(81\) Calculate or simplify the expression \( \sqrt(0.36) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{0.36}\) - step1: Rewrite the expression: \(\sqrt{\frac{9}{25}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{9}}{\sqrt{25}}\) - step3: Simplify the expression: \(\frac{3}{5}\) Calculate or simplify the expression \( 4^2 \). Calculate the value by following steps: - step0: Calculate: \(4^{2}\) - step1: Evaluate the power: \(16\) Calculate or simplify the expression \( \sqrt(4) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{4}\) - step1: Write in exponential form: \(\sqrt{2^{2}}\) - step2: Simplify the root: \(2\) Calculate or simplify the expression \( (1)^3 \). Calculate the value by following steps: - step0: Calculate: \(1^{3}\) - step1: Evaluate the power: \(1\) Calculate or simplify the expression \( \sqrt(400) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{400}\) - step1: Write in exponential form: \(\sqrt{20^{2}}\) - step2: Simplify the root: \(20\) Calculate or simplify the expression \( \sqrt(0.01) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{0.01}\) - step1: Rewrite the expression: \(\sqrt{\frac{1}{100}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{1}}{\sqrt{100}}\) - step3: Simplify the expression: \(\frac{1}{10}\) Calculate or simplify the expression \( (1000000)^(1/3) \). Calculate the value by following steps: - step0: Calculate: \(1000000^{\frac{1}{3}}\) - step1: Factor the number: \(\left(100^{3}\right)^{\frac{1}{3}}\) - step2: Evaluate the power: \(100\) Calculate or simplify the expression \( (0.008)^(1/3) \). Calculate the value by following steps: - step0: Calculate: \(0.008^{\frac{1}{3}}\) - step1: Convert the expressions: \(\left(\frac{1}{125}\right)^{\frac{1}{3}}\) - step2: Use the properties of exponents: \(\frac{1^{\frac{1}{3}}}{125^{\frac{1}{3}}}\) - step3: Evaluate the power: \(\frac{1}{125^{\frac{1}{3}}}\) - step4: Evaluate the power: \(\frac{1}{5}\) Calculate or simplify the expression \( (1/27)^(1/3) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{1}{27}\right)^{\frac{1}{3}}\) - step1: Use the properties of exponents: \(\frac{1^{\frac{1}{3}}}{27^{\frac{1}{3}}}\) - step2: Evaluate the power: \(\frac{1}{27^{\frac{1}{3}}}\) - step3: Evaluate the power: \(\frac{1}{3}\) Calculate or simplify the expression \( \sqrt(16) * \sqrt(16) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{16}\times \sqrt{16}\) - step1: Use the properties of radicals: \(\sqrt{16\times 16}\) - step2: Multiply the numbers: \(\sqrt{256}\) - step3: Write in exponential form: \(\sqrt{16^{2}}\) - step4: Simplify the root: \(16\) Calculate or simplify the expression \( 2^3 * 3^2 \). Calculate the value by following steps: - step0: Calculate: \(2^{3}\times 3^{2}\) - step1: Expand the expression: \(8\times 3^{2}\) - step2: Expand the expression: \(8\times 9\) - step3: Multiply the numbers: \(72\) Calculate or simplify the expression \( 2^3 * 2^3 \). Calculate the value by following steps: - step0: Calculate: \(2^{3}\times 2^{3}\) - step1: Multiply: \(2^{3+3}\) - step2: Add the numbers: \(2^{6}\) - step3: Evaluate the power: \(64\) Here are the calculations for the problems you provided: ### 1. Squares of the Numbers a) \( 11^2 = 121 \) b) \( 30^2 = 900 \) c) \( 0.5^2 = 0.25 \) d) \( 12^2 = 144 \) e) \( 80^2 = 6400 \) f) \( 100^2 = 10000 \) g) \( \left(\frac{2}{5}\right)^2 = \frac{4}{25} \) h) \( \left(\frac{3}{7}\right)^2 = \frac{9}{49} \) ### 2. Cubes of the Numbers a) \( 10^3 = 1000 \) b) \( 0.2^3 = 0.008 \) c) \( 5^3 = 125 \) d) \( 40^3 = 64000 \) e) \( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) f) \( \left(\frac{2}{3}\right)^3 = \frac{8}{27} \) ### 3. Values of the Numbers a) Square of 9: \( 9^2 = 81 \) b) Square root of 9: \( \sqrt{9} = 3 \) c) Square of 4: \( 4^2 = 16 \) d) Square root of 4: \( \sqrt{4} = 2 \) e) Cube of \( 1^{-} \): \( 1^3 = 1 \) ### 4. Without Using a Calculator a) \( \sqrt{400} = 20 \) b) \( \sqrt{0.01} = 0.1 \) c) \( \sqrt{0.36} = 0.6 \) d) \( \sqrt[3]{0.008} = 0.2 \) e) \( \sqrt[3]{\frac{1}{27}} = \frac{1}{3} \) f) \( \sqrt[3]{1000000} = 100 \) ### 5. Calculations a) \( 2^3 \times 3^2 = 8 \times 9 = 72 \) b) \( \sqrt{16} \times \sqrt{16} = 4 \times 4 = 16 \) c) \( 2^3 \times 2^3 = 8 \times 8 = 64 \) d) \( \sqrt{25} \times \sqrt{25} = 5 \times 5 = 25 \) If you have any further questions or need additional calculations, feel free to ask!