50 ! simplify each expression. use positive exponents. 1. a^4b^-3/ab^-2 2. (x^-2y^-4x^3)^-2

1. a^3 / b

For the exponents of a: a^4/a^1 = a^(4-1) = a^3
For the exponents of b: b^-3 / b^-2 = b^(-3--2) = b^-1 = 1/b

2. y^8 / x^2

For the exponents of y: (y^-4)^-2 = y^(-4*-2) = y^8
For the exponents of x: (x^-2 * x^3) = x^(-2+3) = x^1
(x^1)^-2 = x^-2 = 1/x^2

To solve this question, note that multiplying will add exponents and dividing will subtract exponents, and x^-1 is equal to 1/x.