Using Exponents in Algebra

You might like to read the page on Exponents first.

Whole Number Exponents

The exponent "n" in an says how many times to use a in a multiplication:

  exponent definition

Example: 53 = 5 × 5 × 5 = 125

  • The "3" says to use 5 three times in a multiplication
  • In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

Negative Exponents

negative-exponent

A negative exponent a−n is equal to 1/an (1 divided by the positive exponent)

Example: 5−3 = 1/53 = 1/125 = 0.008

 

Also ... by just changing the signs of the exponents we get:−

negative-exponent

A positive exponent an is equal to 1/a−n (1 divided by the negative exponent)

 

So, we can move an expression between the top and bottom (numerator and denominator) of a fraction by simply changing the sign of the exponent.

Example: x−1 = 1/x (a simple reciprocal)

Example: 5−3 = 1/53 = 1/125 = 0.008