## Multiplying Exponents

**Exponents**, sometimes called “powers,” are a simple way of showing repeated multiplication. As an example, multiply five by itself four times, as in 5 ✕ 5 ✕ 5 ✕ 5. Another way to express this would be as “five raised to the fourth power,” or 5^{4}. In this example, the five is called the **base **and the four is called the **exponent**. The exponent is the number of times the base is multiplied by itself. To find the value of an exponent, simply perform the multiplication: 5 ✕ 5 = 25; 25 ✕ 5 = 125, and 125 ✕ 5 = 625. Therefore, 5^{4} = 625.

You must learn the rules for basic operations involving exponents. The rules for multiplication with exponents are summarized below:

- To multiply two terms with the same base and different exponents, keep the base the same and add the exponents:
*x*=^{y}x^{z}*x*^{y + z}**Example**: 2^{2}(2^{3}) = 2^{2 + 3}= 2^{5}= 32 - To simplify an exponential term that has one base and two exponents, multiply the exponents: (
*x*)^{y}^{z}=*x*^{yz}**Example**: (2^{2})^{3}= 2^{2 × 3}= 2^{6}= 64