How do you simplify #(-(2/3))^-2#?

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Answer 1 · 2016-09-11T13:42:39

The result is #9/4# or #2 1/4#

#(-(2/3))^(-2)=(-3/2)^2=9/4#

In the calculation I used the following property of powers:

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

Answer 2 · 2016-09-11T13:43:22

#(9) / (4)#

We have: #(- ((2) / (3)))^(- 2)#

First, let's expand the parentheses:

#= (- (2) / (3))^(- 2)#

Then, using the laws of exponents:

#= (1) / ((- (2) / (3))^(2))#

#= (1) / (((- 2) / (3))^(2))#

#= (1) / (((- 2)^(2) / (3)^(2)))#

#= (1) / (((4) / (9)))#

#= 1 cdot ((9) / (4))#

#= (9) / (4)#