How do you simplify 7^sqrt2*7^(3sqrt2)?

${7}^{4 \setminus \sqrt{2}}$

Explanation:

Powers on the same base, are added in the multiplication as follows

${7}^{\setminus \sqrt{2}} \setminus \cdot {7}^{3 \setminus \sqrt{2}}$

$= {7}^{\setminus \sqrt{2} + 3 \setminus \sqrt{2}}$

$= {7}^{4 \setminus \sqrt{2}}$