Short Answer: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents (-33xy^-1/66x^0y^-3)^2
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To simplify the expression ((-33xy^(-1))/(66x^(0)y^(-3)))^2, we follow these steps:
Step 1: Simplify any negative exponents by moving the terms to the opposite position in the fraction. A negative exponent means that we need to take the reciprocal of the term. In this case, we need to move y^(-1) and y^(-3) to the denominator:
((-33x)/(66xy^3))^2
Step 2: Combine like terms in the numerator and denominator:
((-1/2)x/y^3)^2
Step 3: Square each term separately:
((-1/2)^2 * x^2)/(y^3)^2
Step 4: Simplify further by evaluating the exponents:
((1/4)x^2)/(y^6)
Thus, the simplified expression is (1/4)x^2/y^6.