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##### What is solution of (-x)^-n (n is for all integer)...? ____________________________________

##### Explanation

We should must be careful about order of operations when using negative numbers or negative exponents.

```                      -n
Before solution of (-1)
```

Let us see the solution of -1 base to power 2 and 3.

```We know that
2
(-1)  = 1
And
3
(-1)  = -1
```

therefore -1 to any EVEN power is 1 and -1 to any ODD power is -1. By putting this rule to all integers. We get ...

```                                          _
n                                  |
(-x) = 1      if n is EVEN             |
n                                   >
(-x) = -1     if n is ODD              |
_|

Similarly
-n      1        1                _
(-x)   = ------- = ----  if n is EVEN  |
n      x                 |
(-x)                         |
|
-n      1       1                   >
(-x)   = ------ = ----   if n is ODD   |
n    -x                  |
(-x)                         |
_|
```

Final answer will be 1/x when n is EVEN and -1/x when n is ODD.

Here we should must be careful about the negative exponents. First convert into positive exponent and then solve further.

____________________________________

##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     