Final answer:
An expression with a base and an exponent is referred to as exponential notation, with the base being the number that is multiplied by itself as many times as indicted by the exponent. Exponential arithmetic simplifies the representation of large and small numbers.
Step-by-step explanation:
An expression that uses a base and an exponent is known as exponential notation or simply an exponent. For example, in the expression 5², the number 5 is the base and the 2 is the exponent. This tells us to multiply the base by itself the number of times indicated by the exponent, so 5² is 5 x 5, which equals 25. Exponential notation is especially helpful when dealing with very large or very small numbers, allowing them to be written more compactly.
Knowing how to work with exponents is crucial in mathematics. For example, when you multiply two values with the same base, you add the exponents. However, this rule only applies when the bases are the same. Moreover, other operations such as raising an exponent to another power, multiplying two exponentiated pieces together, or dealing with negative exponents, have specific rules that make calculations easier and more straightforward.