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

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##### 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