The rules are described in plain English (as close to plain English as we get in math). To see the the process written out in proper form, watch the video.

 

• Multiplying: something to the power m times the same thing to the power n is that something to the power of m plus n.

• Dividing: something to the power m divided by the same thing to the power n is that something to the power of m minus n.

• Powers of powers: something to the power m all to the power n is the something to the power of m times n.

• Two things multiplied together, raised to an exponent each inherit the exponent. So a times b all to the power n becomes a to the n, b to the n.

• For a fraction with an exponent, both the top and bottom inherit the exponent: a over b to the n becomes a to the n over b to the n.

• Power one: anything to the power one just stays the same.

• Power zero: anything to the power zero is one, it doesn’t matter what the something was to begin with, positive or negative, it will still just be one.

• Power negative one: means the reciprocal or one over the something.

• Powers of negative n: means the reciprocal with the exponent n.

• Fractions to the power of negative n: means take the reciprocal then give out the exponent to both the top and bottom.

• Power one half: the same as a square root sign

• Power one third: same as a cube root sign... and so on

• Power of four over five: the four is an exponent, the five is a root. So to the power four, fifth root.