Question 1152124: How to solve (2/3)^-2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
https://www.mathsisfun.com/algebra/exponent-laws.html
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.
https://www.purplemath.com/modules/exponent.htm
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