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[ (-2)^-2 + (-3)^-1 ]^-1 =...?

________________________________

Answer

-12

Explanation
                      -1   
     _              _           
    |   -2        -1 |
    |(-2)    + (-3)  |
    |_              _|

Solve the outer exponent first. We know that a^-1 = 1/a

            1
    = -------------
         -2      -1 
      (-2)  + (-3)  
    
            1
    = ---------------
        1        1 
      ----  -  -----
         2      
      (-2)       3  

            1
    = ---------------
        1        1 
      ----  -  -----
        4        3 
             
           1
    = ------------
        3  -  4
       ---------
          12        

          1
    = ---------
         -1
       ------
         12      
      
             12
    = 1 × - ---
             1

    = -12

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  • Solve
                 _____________________
                /      _____________  
               /     /        ____
              /     /        /  2  
             /  4  /  4  .  / 4  
            /    \/       \/
           /  --------------------
          /            3
        \/            2    
    
        
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