Exponents
Exponentiation means raising to a power of a real number. For example: 2^3 = 2 * 2 * 2.
Integer Exponents
Integer exponents are cases in which the powers are positive or negative whole numbers.
An example of a positive exponent is if a is any real number and n is any positive integer, then by a^n we mean the quantity of a * a * * * * a (n times). thus, a^1 = a, a^2 = a * a, and so forth. Here with the expression a^n the number n is the exponent and the number a is called the base.
Negative exponents exist for example if a is any real number other than zero and n is any positive integer. (i.e. a^-1 = 1 / a ^n = 1 / a * a * * * * (n times) )
Zero exponents are where a is any real number other than zero: (i.e. a ^0 = 1 )
When combining exponential expressions, we use the following identities:
- a^m * a^n = a^m+n
- a ^m / a^n = a ^ (m – n) (if a is not equal to zero)
- (a^n) ^ m = a ^ (n * m)
- (ab) ^ n = (a ^ n) * (b ^ n)
- (a / b ) ^n = a ^ n / a ^ m (if b is not equal to zero)
In the first two identities the base expression cannot be the same
Do not invent your own identities.