9) \( \sqrt[3]{1} \cdot \sqrt[3]{\frac{1}{49}}-0,6: 0,4(0,3)^{-1}+1, \overline{7}= \)

Let's break it down step by step: 1. Calculate \( \sqrt[3]{1} \cdot \sqrt[3]{\frac{1}{49}} \): - \( \sqrt[3]{1} = 1 \) - \( \sqrt[3]{\frac{1}{49}} = \sqrt[3]{49^{-1}} = \frac{1}{\sqrt[3]{49}} \) - Knowing \( \sqrt[3]{49} = \sqrt[3]{7^2} = 7^{2/3} \), we have \( \sqrt[3]{\frac{1}{49}} = 7^{-2/3} \). - Therefore, \( 1 \cdot 7^{-2/3} = 7^{-2/3} \). 2. Calculate \( 0.6 : 0.4(0.3)^{-1} \): - \( 0.6 : 0.4 = \frac{0.6}{0.4} = 1.5 \). - \( (0.3)^{-1} = \frac{1}{0.3} = \frac{10}{3} \). - Thus, \( 1.5 \cdot \frac{10}{3} = 5 \). 3. Now combine the parts: - \( 7^{-2/3} - 5 + 1 = 7^{-2/3} - 4 \). Furthermore, \( \overline{7} \) meaning repeating 7 as in \( 1.777... \) which is \( \frac{16}{9} \). Finally, putting it all together: - Therefore, you need to calculate \( 7^{-2/3} - 4 + 1.777... \). - This continues as \( \sqrt[3]{\frac{1}{49}} - 3.222...\). This results in a complex expression; you can numerically evaluate it based on the decimal or keep it in rational form! Happy solving!