Rational exponents and radicals are simplified in a similar way to how other exponents and radicals are simplified.
For the first expression 4x⁻⁴y⁴, you can simplify it by noticing that it has a negative exponent on the x term and a positive exponent on the y term. To simplify, you can keep the base (x and y) and the exponent (4 and -4) but you change the negative exponent to a fraction and change the sign:
4x⁻⁴y⁴ = (x^-4) (y^4) = x^-4y^4
For the second expression -2x⁴y⁻¹, you can simplify it by noticing that it has a negative exponent on the y term. To simplify, you can keep the base (x and y) and the exponent (4 and -1) but you change the negative exponent to a fraction and change the sign:
-2x⁴y⁻¹ = -2 (x^4) (y^-1) = -2x^4y^-1
To simplify these expressions further, you would need to know the specific values of x and y. But these are the steps to simplify a rational exponent or radical to its simplest form.
It's also worth mentioning that if you have a fractional exponent you can simplify it by raising the base to the numerator of the exponent and the denominator of the exponent. For example, x^(3/4) = (x^3)^(1/4) = ∛x
Keep in mind that when you simplify rational exponents or radicals, you should always keep the base and the exponent, and only change the sign of the exponent if it is negative.