2.1 Use the language of algebra  (Page 4/8)

We say $2^3$ is in exponential notation and $2·2·2$ is in expanded notation.

Exponential notation

For any expression $a^n,a$ is a factor multiplied by itself $n$ times if $n$ is a positive integer.

$a^n\text{means multiply}n\text{factors of}a$

The expression $a^n$ is read $a$ to the $n^{th}$ power.

For powers of $n=2$ and $n=3,$ we have special names.

[link] lists some examples of expressions written in exponential notation.

To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.

Simplify expressions using the order of operations

We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations . Otherwise, expressions may have different meanings, and they may result in different values.

For example, consider the expression:

Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.

Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. P lease E xcuse M y D ear A unt S ally.