Simplify ((3p^3q^-1)/(9p^2q^-2))^2

Problem

((3*p3*q(−1))/(9*p2*q(−2)))2

Solution

1. Simplify the fraction inside the parentheses by dividing the coefficients and applying the quotient rule for exponents, am/an=a(m−n)

(3*p3*q(−1))/(9*p2*q(−2))=1/3*p(3−2)*q(−1−(−2))

2. Perform the subtraction in the exponents to simplify the expression further.

1/3*p1*q1=(p*q)/3

3. Apply the power rule (a/b)n=an/bn to the simplified fraction.

((p*q)/3)2=((p*q)2)/3

4. Distribute the exponent to each factor in the numerator and evaluate the denominator.

(p2*q2)/9

Final Answer

((3*p3*q(−1))/(9*p2*q(−2)))2=(p2*q2)/9

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