What property does this indicate?

Question

((√a⁷)^{-b^5})((√a⁷)^{+b^5})=a⁷-b¹⁰

Answer 1

I am guessing that you mean [ (√a⁷) - b⁵ ] [ (√a⁷) + b⁵ ] = (√a⁷)² - (b⁵)² = a⁷ - b¹⁰

This is an example of the Difference of Two Squares Formula (DOTS): (X - Y)(X + Y) = X² - Y²

Answer 2

The laws of exponents: Same base, different exponents, multiplied.

( X^{-b^5} ) * ( X^{b^5} ) = X⁰ = 1 if X≠0

and undefined if X=0.

The fact that X = √a⁷ is irrelevant.