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##### What is relation between positive and negative exponent...? ____________________________________

##### Explanation

Each number has its reciprocal. For example reciprocal of 5 is 1/5 and reciprocal of 7 is 1/7. Also notice that multiplication of 5 and 1/5 is 1.

```         1
5 . --- = 1
5
1
7 . --- = 1
7

Now let we have
n
x

Its reciprocal is
1
----
n
x

-n
= x

Which is a negative exponent.

Now multiplication of x^n and x^-n is also 1
n   -n   n-n    0
x . x  = x    = x = 1

n                        -n
So x   is the reciprocal of x

```

Now 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, i.e.

```                   n
n     -n     x
x  ×  x   = ------ ........(i)
n
x
```

Similarly multiplication of x to power -n and its reciprocal x to power n is same as division of x to power n by x to power n, i.e.

```                   n
-n     n     x
i.e x  ×  x   = ------........(ii)
n
x

From (i) & (ii)
n
-n     n    n     -n      x
x  ×  x   = x  ×  x   = ------ = 1
n
x

Therefore x^n and x^-n is are reciprocal 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. Positive exponent and negative exponet are reciprocal of each other.
2. Positive exponent and Negative exponent 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     