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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-------------- = ?
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Solve
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