Raise the quantity in parentheses to the indicated exponent and simplify the resulting expression with positive exponents.
((-27x^0 y^(-2))/(54x^(-5) y^(-4) ))^(-2)
x^0 = 1, so you have
(54x^(-5) y^(-4))^-2 = 54x^10 y^8
-27y^-2 / 54x^10y^8 = -1/2x^10y^10 = -1/2 (xy)^-10
Starting out with almost all negative exponents, I don't see how you can wind up with positive exponents. Also, any value with a zero exponent = 1.
To raise the quantity in parentheses to the indicated exponent and simplify the resulting expression with positive exponents, we follow these steps:
Step 1: Simplify the expression inside the parentheses first.
Inside the parentheses, we have:
(-27x^0 y^(-2))/(54x^(-5) y^(-4))
Simplifying this expression:
-27x^0 y^(-2) = -27(1)/(y^2) = -27/y^2
54x^(-5) y^(-4) = 54/(x^5 y^4)
So, the expression becomes:
((-27/y^2)/(54/(x^5 y^4)))^(-2)
Step 2: Invert and multiply.
To raise the fraction to a negative exponent, we can invert it and change the sign of the exponent.
Therefore, the expression becomes:
((-27/y^2)(x^5 y^4)/54)^2
=(-27x^5 y^4)/(y^2*54))^2
=(-27x^5 y^4)/54^2
Step 3: Simplify the expression with positive exponents.
54^2 = 2916, so the expression becomes:
(-27x^5 y^4)/2916
Therefore, the simplified expression is:
(-27x^5 y^4)/2916.