[tex] {5}^{4 + 2 \sqrt{2} } \div {5}^{2 + \sqrt{8} } = {5}^{4 + 2 \sqrt{2} } \div {5}^{2 + 2 \sqrt{2} } = \\ \\ = {5}^{4 + 2 \sqrt{2} - (2 + 2 \sqrt{2} ) } = {5}^{4 + 2 \sqrt{2} - 2 - 2 \sqrt{2} } = {5}^{2} = 25[/tex]
