Laws of Exponents

The laws of exponents refer to a set of rules for multiplying, dividing and even raising exponents to powers to make these operations easier.

The product rule is used to multiply exponents with the same base.  It states that to multiply two numbers with the same base all you do is add their exponents.

Example:  22 · 23 = 25      25=32

2 · 2 · 2 · 2 · 2  = 32

am · an = am+n

The quotient rule is used to divide exponents with the same base.  It states that to divide two numbers with the same base all you do is subtract their exponents.

Example:  105 ¸ 103 = 102      102=100

105=100,000

103=1,000

100,000 ¸ 1,000 = 100

am ¸ an = am-n

 3·2=6

The power rule is used to raise a number already written as an exponent to another power.  It states that to raise an exponent to a power you multiply the exponents.

Example:        (33)2  =  33   ·  33         33   ·  33  = 36

If you wrote this out you would get 3 · 3 · 3 · 3 · 3 · 3 or 36

(am)n = am·n

The power of a product rule is as follows

To find the power of a product, find the power of each factor and multiply

(ab)m= ambm

And the power of a quotient rule is as follows

To find the value of a quotient, find the power of each number and divide.