Final answer:
To simplify the expression (-3xy⁻³y⁻⁵)⁻³ / (x⁴y⁴z⁴)⁻¹, distribute the exponent, simplify the terms, and divide the expressions.
Step-by-step explanation:
To simplify the expression (-3xy⁻³y⁻⁵)⁻³ / (x⁴y⁴z⁴)⁻¹, we can start by distributing the exponent outside the parentheses to each term inside. The negative power outside the parentheses can be turned into a positive power by moving the term to the denominator. This gives us (1/(-3xy⁻³y⁻⁵)³) / (1/(x⁴y⁴z⁴))¹.
Next, we can simplify each term inside the parentheses by using the properties of exponents. We can combine the x terms by subtracting the exponents. (-3x⁴y⁻⁸)³ and (xyz)⁴.
After simplifying the terms, we can divide the two terms by dividing the digit term of the numerator by the digit term of the denominator and subtracting the exponents. This gives us (-3x⁴y⁻⁸)³ / (xyz)⁴.