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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What is relation between positive and negative exponent?
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2n - 2n
-------------- = ?
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2n
Solve
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