What us 6 to the 3rd power times 6 to the negative 3rd power

"6 to the 3rd power" or 6³ means (6 · 6 · 6).

"6 to the negative 3rd power" or 6⁻³ means 1 / (6 · 6 · 6).

When you multiply them, you have

(6 · 6 · 6) / (6 · 6 · 6).

That's a fraction with the exact same thing on top and bottom, and that's 1.