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##### What is relation between x^-n and 1/x^n...? -->

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##### Explanation

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

```      -n    n     -n
If   x  , -x  , -x    then

-n
x    means  x raise to power -n
n
-x   means -x raise to power  n
-n
-x   means -x raise to power -n
```

Any number x raise to a negative power -n is same as 1 over the number raised to positive power n, i.e.

```     -n      1
x   = ------
n
x
```

Similarly any number x raise to a power n is same as 1 over the number raised to negative power n, i.e.

```     n      1
x  = ------
-n
x

```

When apply the addition rule of exponents will still work with negative exponents.

```     n    -n    n+(-n)    n-n    0
x  × x   = x       = x    = x  = 1

-n    n    -n+n      0
x  × x   = x       = x  = 1
```

Therefore x^n and x^-n is are reciprocal of each other and multiplcative inverse of each other.

In other words multiplication of x to power n and its reciprocal x to power -n or multiplication of x to power -n and its reciprocal x to power n is same as dividing x to power n by x to power n.

##### Conclusion

1. x^n and x^-n are reciprocal of each other.
2. x^n and x^-n are multiplcative inverse of each other.

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##### 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     