"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 .
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