# Exponents

An exponent of a number indicates how many times to multiply the number by itself. Exponents are also called powers or indices.

For example: Let’s take a look at the number 95. Here 9 is called the base and 5 is the exponent ( or power or index). You would usually say “9 to the power of 5” or “9 to the fifth exponent”. It tells us that 9 has to be multiplied five times by 9, that is: 95=9·9·9·9·9

## Properties of exponents

 Property Explanation an is a multiplied by itself n times a-1 is the same as 1 divided by an a0 is by definition always 1 Two numbers with the same bases but different exponentsare multiplied together by adding the exponents Two numbers with the same bases but different exponentsare divided by each other by subtracting the exponentsfrom each other. Two numbers with the same exponents but differentbases are multiplied together by multiplying the basesand then raise the result to the exponent If a number with an exponent is the base to an exponent,the two exponents are multiplied together A base, which is raised to the exponent one half,is equal to the square root of the base. A base, which is raised to the exponent one third,is equal to the cubic root of the base. The n-th root of the base a raised to the exponent pis equal to the base a raised to the exponent p/n