Positive indices
a)(xy)^-2
= 1/(xy)^2
b) 5a^-3
= 5/ a^3
c) 3x^2y^3z^-1
= 3x^2y^3/ z
d) b^-4 c^3
= c^3/ b^4
e) (pqrs)^0
= 1 (Anything raised to 0 is 1)
To simplify the expression (xy)^-2, we can apply the rule of positive indices:
(xy)^-2 = 1/(xy)^2
Now, let's simplify the denominator by expanding (xy)^2:
(xy)^2 = (x^2)(y^2)
Finally, substituting this back into our expression, we have:
1/(xy)^2 = 1/(x^2)(y^2)
Therefore, the simplified form of (xy)^-2 is 1/(x^2)(y^2).