Laws of Indices

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.