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. |