An index (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.
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 |
The following demonstration illustrates more of this notation. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.
The index is equal to the number of times the base is multiplied by itself.
State the base for the expression 3^{2}.
Identify the power for the expression 4^{6}.
Evaluate 3^{5} \div 3^{3}.
An index (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.