1.10 Powers of whole numbers
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.
For example, in the expression $$103 the number $$10 is the base term and the number $$3 is the index (or power) term. The expression $$103 is the same as $$10×10×10, or the number $$10 multiplied $$3 times.
Think of the base as that being closest to the ground, and the index (or power) is above.
We often encounter a power of $$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. $$5 with an index (or power) of $$2, can be expressed as $$52, and can be read as "$$5 to the power of $$2" or "five squared".
A number, e.g. $$10 to the power of $$3, can be expressed as $$103, and can be read as "ten cubed". A power of $$3 is involved in calculations like measuring the volume of a cube.
A base to the power of any other number, e.g. $$34, 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.
$$34=3×3×3×3
The following demonstration illustrates more of this notation. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.
Practice questions
Question 1
State the base for the expression $$32.
Question 2
Identify the power for the expression $$46.
$$6
A$$4
B
Question 3
Evaluate $$35÷33.