1. Simplify: (y ^ 2 * x ^ 8)/(x ^ 6 * y ^ 2)
To simplify the expression (y ^ 2 * x ^ 8)/(x ^ 6 * y ^ 2), we can divide the variables and subtract the exponents:
(y ^ 2 * x ^ 8)/(x ^ 6 * y ^ 2) = x^(8-6) * y^(2-2)
Simplifying further, we get:
= x^2 * y^0
Since any number or variable raised to the power of 0 equals 1, we can simplify it as:
= x^2 * 1
Therefore, the simplified expression is:
x^2