1.01 Exponent notation
Ideas
Exponent notation
An exponent (or power) is a small number placed in the upper right hand corner of another number to note how many times a base is being multiplied by itself.
For example, in the expression 10^3 the number 10 is the base term and the number 3 is the exponent (or index or power). The expression 10^3 is the same as 10\times10\times10, or the number 10 multiplied 3 times.
In the above expression, we call 10^3 the exponential form and 10\times10\times10 the expanded form of the expression.
We often encounter a power of 2 when measuring area. Consider the area of a square, for example, which is given by side length times side length. A number, e.g. 5 with an exponent (or power) of 2, can be expressed as 5^2, and can be read as "5 to the power of 2" or "five squared".
A number, e.g. 10 to the power of 3, can be expressed as 10^3, and can be read as "ten cubed". A power of 3 is involved in calculations like measuring the volume of a cube.
A base to the power of any other number, e.g. 3^4, can be read as "three to the power of four", and means that the base number is multiplied by itself the number of times shown in the power.
| \displaystyle 3^4 | \displaystyle = | \displaystyle 3\times3\times3\times3 |
Exploration
The following demonstration illustrates more of this notation. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.
As the value of the exponent changes, describe what happens to the number of times the base is multiplied.
Examples
Example 1
State the base for the expression 3^2.
Example 2
Identify the power for the expression 4^6.
Example 3
Write the following in expanded form: 7^5 \times 6^4
An exponent (or power) notes how many times a base is being multiplied by itself.
A base to the power of any other number means that the base number is multiplied by itself the number of times shown in the power.