To multiply numbers with the same base, keep the base and add the indices. 

To divide numbers with the same base, keep the base and subtract the indices. 

When raising a power to a power, keep the base and multiply the indices. 

The power of a product is the product of the powers. 

A power of a quotient is the quotient of the powers. 

The root of a quotient is the quotient of the roots . 

The root of a quotient raised to a power is the quotient of the roots of the powers. 

(is not defined) 
Any nonzero number raised to the power of zero is 1. 
and 
A negative exponent means take the reciprocal. 
A root is a fractional power. Taking the nth root is the same as raising to the power 

Using the third and seventh rules allows us to raise a root to a power. 