Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc
Here we provide thousands of Question and their ANSWERS. Our question is helpful in ECAT, UPSC(IAS/IPS/IFS), ESE, EES, NTS FSc, BSc and all kinds of MATH/IQ TESTS.
You should must be careful about order of operations when using negative numbers or negative exponents.
-n n -n
If x , -x , -x then
x means x raise to power -n
-x means -x raise to power 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.
x = ------
Similarly any number x raise to a power n is same as 1 over the number raised to negative power n, i.e.
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.
1. x^n and x^-n are reciprocal of each other. 2. x^n and x^-n are multiplcative inverse of each other.
2n - 2n
-------------- = ?
/ / ____
/ / / 2
/ 4 / 4 . / 4
/ \/ \/