Exponents

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  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 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:

  1. a^m * a^n = a^m+n
  2. a ^m / a^n = a ^ (m – n) (if a is not equal to zero)
  3. (a^n) ^ m = a ^ (n * m)
  4. (ab) ^ n = (a ^ n) * (b ^ n)
  5. (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.

 

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