Lesson 1: Exponent Review

Property

For any expression $a^n$, $a$ is a factor multiplied by itself $n$ times if $n$ is a positive integer.
The expression $a^n$ is read $a$ to the $n^{th}$ power. In $a^n$, the $a$ is called the base and the $n$ is called the exponent.
$a^n = a \cdot a \cdot a \cdot ... \cdot a$ ($n$ factors)
Special names are used for powers of 2 and 3:
$a^2$ is read as '$a$ squared'
$a^3$ is read as '$a$ cubed'

Examples

• The expression $5 \cdot 5 \cdot 5 \cdot 5$ can be written in exponential notation as $5^4$, where 5 is the base and 4 is the exponent.
• To write $y^3$ in expanded form, you write out the base $y$ multiplied by itself 3 times: $y \cdot y \cdot y$.
• To simplify $2^5$, you calculate $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$, which equals $32$.

Explanation

Exponents are a shortcut for writing repeated multiplication. The small exponent number tells you how many times to multiply the larger base number by itself. This makes it much faster to write out long calculations involving the same factor.

Property

An exponent on a variable indicates repeated multiplication, while a coefficient in front of a variable indicates repeated addition.

but

Examples

• For the variable $y$, the expression $y^3$ means $y \cdot y \cdot y$.

• For the same variable $y$, the expression $3y$ means $y+y+y$.

Property

Evaluate expressions involving powers by substituting specific values for variables.
A power is an expression of the form $a^n$ where $a$ is the base and $n$ is the exponent.
To evaluate, replace the variable with its given value and calculate the result.

Examples