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Exponential Terms With Negative Base

In this chapter we are going to learn the concept of exponential terms with base negative which means

the base number is negative, for instance (-3)4.
 
Let us try to solve the example, for a while assume -3 as 3 and now 3 is multiplied itself for 4 times,
i.e., 3 x 3 x 3 x 3 we get 81. We got 81 for 34, now depend on the exponent (even or odd) we get the final result.
Exponent 4 is even, thus (-3)4 is 81.
 
Therefore we get the result for (-3)4 as 81.
 
Let us try to solve one more example taking the exponent odd, i.e., (-2)7
For sometime assume -2 as 2, now 2 is multiplied itself for 7 times, i.e., 2 x 2 x 2 x 2 x 2 x 2 x 2,
we get as 128 for 27.
Depend on the exponent (even or odd) we get the final result for (-2)7 here we have 7 which is odd.
Thus we get the result as negative for  (-2)7 .
Therefore we get the result for (-2)7 as -128.
 
Few more examples :

  1. (1)4 = 1 x 1 x 1 x 1 = 1
  2. (1)3 = 1 x 1 x 1 = 1
  3. (-1)3 = (-1) x (-1) x ( -1) =  -1
  4. (-1)4 = (-1) x (-1) x (-1) x (-1) = 1
  5. (-1)5 = (-1) x (-1) x (-1) x (-1) x (-1) = -1

 
The below concept is to be remembered :
 

  • If (-a)m= -am , m is odd
  • If (-a)m = am , m is even
  •  

    Let us try to solve few more examples :

    1. (-3)4

    2. (-a)4
    3. (-5)-3

     
    In the first example (-3)4 = (-3) x (-3) x (-3) x (-3) = 81
     
    Therefore the result for (-3)4 = 81.
     
    Coming to second example (-a)4 = (-a) x (-a) x (-a) x (-a) = a4.
     
    Therefore the result for (-a)4 = a4.
    Therefore the result for (-5)-3 = -1/125.
     
    In the last example (-5)-3 = 1/(-5)3 = -(1)/125.    ( since a-m = 1/am)
    The examples have been illustrated in the video below  :

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