Which expression is equivalent to [(3xy^-5)^3 / (x^-2y^2)^-4]^-2
Accepted Solution
A:
The answer is (x¹⁰y¹⁴)/729.
Explanation: We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us
[(3³x³y⁻¹⁵)/(x⁸y⁻⁸)]⁻².
Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have [(3³x³y⁸)/(x⁸y¹⁵)]⁻².
Using the quotient property, we subtract exponents when dividing powers, which gives us (3³/x⁵y⁷)⁻².
Evaluating 3³, we have (27/x⁵y⁷)⁻².
Using the power of a power property again, we have 27⁻²/x⁻¹⁰y⁻¹⁴.
Flipping the negative exponents again gives us x¹⁰y¹⁴/729.