Question 1152124
the easiest way to solve this is to follow the rule that states:


(a/b)^-c = 1 / (a/b)^c


then there is the rule that states:


(a/b)^c = a^c / b^c


there is also the rule that states:


1 / (a^c / b^c) = b^c / a^c


using these three rules, you would get:


(2/3)^2 = 1 / (2/3)^2 = 1 / (2^2 / 3^2) = 3^2 / 2^2 = 9/4 = 2.25


here's a reference on exponent arithmetic rules.


<a href = "https://www.mathsisfun.com/algebra/exponent-laws.html" target = "_blank">https://www.mathsisfun.com/algebra/exponent-laws.html</a>


notice, he did not give you (x/y)^-n.


however, he did give you x^-n = 1/x^n


the x in this case, doesn't just refer to a variable.
it also refers to an expression.


in this case x represents the expression of (a/b).


when he says x^n = 1/x^-n, when you replace x with a/b, you get (a/b)^-n = 1/(a/b)^n


the a/b within parentheses makes that expression act like a variable until you break it out of the parentheses.


(a/b)^-n = 1/(a/b)^n = 1/(a^n/b^n) = b^n / a^n


here's another reference that is more detailed and also more informative.


<a href = "https://www.purplemath.com/modules/exponent.htm" target = "_blank">https://www.purplemath.com/modules/exponent.htm</a>