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 non-zero 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.