Simplify algebraic expressions involving exponents.

For the first problem, use the rule $a^m / a^n = a^{m-n}$ to get $x^{1-7} = x^{-6} = 1/x^6$. For the second problem, apply the power of a product rule $(abc)^n = a^n b^n c^n$ and the power of a power rule $(a^m)^n = a^{mn}$ to get $(-2)^2 (x^3)^2 (y^4)^2 = 4x^6y^8$.