1.3. Simplify the following without the aid of a calculat 1.3.1. \( \left(3,6 \times 10^{6}\right)-\left(5,2 \times 10^{5}\right) \) 1.3.2. \( \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} \) 1.3.3. \( \sqrt{\sqrt{(16)^{2}}}-\frac{3}{4} \) 1.3.4. \( \left(7^{-2}+7^{-1}\right) \div(21 \div 3) \)

**1.3.1. Calculation** We have \[ 3.6 \times 10^{6} - 5.2 \times 10^{5}. \] Express \(3.6 \times 10^6\) in terms of \(10^5\): \[ 3.6 \times 10^6 = 36 \times 10^5. \] Thus, the expression becomes \[ (36-5.2) \times 10^5 = 30.8 \times 10^5. \] We can write \(30.8 \times 10^5\) in scientific notation as \[ 3.08 \times 10^6. \] --- **1.3.2. Calculation** We need to simplify \[ \frac{1}{2} + 2\frac{3}{4} - \frac{3}{8}. \] First, convert the mixed number \(2\frac{3}{4}\) to an improper fraction: \[ 2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}. \] Next, add \(\frac{1}{2}\) and \(\frac{11}{4}\) by writing \(\frac{1}{2}\) as \(\frac{2}{4}\): \[ \frac{2}{4} + \frac{11}{4} = \frac{13}{4}. \] Now subtract \(\frac{3}{8}\). Express \(\frac{13}{4}\) with denominator 8: \[ \frac{13}{4} = \frac{26}{8}. \] Then, \[ \frac{26}{8} - \frac{3}{8} = \frac{23}{8}. \] --- **1.3.3. Calculation** We wish to simplify \[ \sqrt{\sqrt{(16)^2}} - \frac{3}{4}. \] First, compute \((16)^2\): \[ (16)^2 = 256. \] Take the first square root: \[ \sqrt{256} = 16. \] Then take the square root of \(16\): \[ \sqrt{16} = 4. \] Finally, subtract \(\frac{3}{4}\): \[ 4 - \frac{3}{4} = \frac{16}{4} - \frac{3}{4} = \frac{13}{4}. \] --- **1.3.4. Calculation** We must simplify \[ \left( 7^{-2} + 7^{-1} \right) \div (21 \div 3). \] First, simplify the numerator: \[ 7^{-2} + 7^{-1} = \frac{1}{7^2} + \frac{1}{7} = \frac{1}{49} + \frac{1}{7}. \] Express \(\frac{1}{7}\) with denominator 49: \[ \frac{1}{7} = \frac{7}{49}. \] Then, \[ \frac{1}{49} + \frac{7}{49} = \frac{8}{49}. \] Now, simplify the denominator: \[ 21 \div 3 = 7. \] Thus, the overall expression becomes \[ \frac{8}{49} \div 7 = \frac{8}{49} \times \frac{1}{7} = \frac{8}{343}. \]