Let's Break it Down
You know that multiplication represents repeated addition of the same number. For example, the multiplication problem \( 3 \cdot \frac{1}{2} \) is the same as the addition problem \( \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \). Writing repeated addition as a multiplication problem shortens both the notation and the solving process.
There is also a shortcut to represent repeated multiplication of the same factor. It is called exponential notation.
Exponential Notation
Exponential notation involves a base and an exponent and is expressed as \( \textsf{base}^{\textsf{exponent}} \).
The base is the factor that is being multiplied by itself.
The exponent is the number of times you multiply the base by itself.
For Example
Write the multiplication problem \( 4 \cdot 4 \cdot 4 \) using exponential notation.
In the multiplication problem \( 4 \cdot 4 \cdot 4 \), the base is 4.
You are multiplying the base, 4, by itself 3 times, so the exponent is 3.
In exponential notation, \( 4 \cdot 4 \cdot 4 = 4^{3} \).
When a number is expressed using exponential notation, you can simply carry out the multiplication to simplify it.
Simplify \( 2^{4} \).
In the exponential notation \( 2^{4} \), the number 2 is the base and the number 4 is the exponent. This notation is the same as \( 2 \cdot 2 \cdot 2 \cdot 2 \). |
Multiply the number 2 by itself 4 times in order to simplify \( 2^{4} \). \( 2^{4} = 2 \cdot 2 \cdot 2 \cdot 2 = 16 \) |
Think you got it?
How well can you work with exponential notation? Use these flashcards to practice. Use your knowledge of exponential notation to answer each question, then click the card to see if you are correct.
Simplify \( 3^{2}. \)
\( 9 \)
The notation \( 3^{2} = 3 \cdot 3 = 9 \).
Write \( 5^{4} \) using repeated multiplication.
\( 5 \cdot 5 \cdot 5 \cdot 5 \)
The base is 5, and the exponent is 4. This means to multiply the number 5 by itself 4 times.
Write the multiplication problem \( 13 \cdot 13 \cdot 13 \) using exponential notation.
\( 13^{3} \)
The base is 13, and the exponent is 3 since the number 13 appears 3 times as a factor.
Write the multiplication problem \( 8 \cdot 8 \cdot 8 \cdot 8 \) using exponential notation.
\( 8^{4} \)
The base is 8, and the exponent is 4.
In the exponential notation \( 1^{9}, \) which number is the base?
1
Exponential notation has the form \( \textsf{base}^{\textsf{exponent}} \).
Simplify \( 7^{3} \).
\( 343 \)
The notation \( 7^{3} \) is the same as \( 7 \cdot 7 \cdot 7 = 343 \).
Write the multiplication problem \( 10 \cdot 10 \) using exponential notation.
\( 10^{2} \)
The base is 10, and the exponent is 2.
Write \( 9^{3} \) using repeated multiplication.
\( 9 \cdot 9 \cdot 9 \)
The base is 9, and the exponent is 3.
In the exponential notation \( 11^{5}, \) which number is the exponent?
5
Exponential notation has the form \( \textsf{base}^{\textsf{exponent}} \).
Simplify \( 5^{3} \).
\( 125 \)
The notation \( 5^{3} \) is the same as \( 5 \cdot 5 \cdot 5 = 125 \).
Cards remaining:
