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Middle Years

1.06 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 $10^3$103 the number $10$10 is the base term and the number $3$3 is the index (or power) term. The expression $10^3$103 is the same as $10\times10\times10$10×10×10, or the number $10$10 multiplied $3$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$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$5 with an index (or power) of $2$2, can be expressed as $5^2$52, and can be read as "$5$5 to the power of $2$2" or "five squared".

A number, e.g. $10$10 to the power of $3$3, can be expressed as $10^3$103, and can be read as "ten cubed". A power of $3$3 is involved in calculations like measuring the volume of a cube.


Base and power

A base to the power of any other number, e.g. $3^4$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.


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 $3^2$32.

Question 2

Identify the power for the expression $4^6$46.

  1. $6$6




Question 3

Evaluate $3^5\div3^3$35÷​33.

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