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The square of a number is that number times itself. 5 squared, denoted
5^{2}
, is equal to
5×5
, or 25. 2 squared is
2^{2} = 2×2 = 4
.
One way to remember the term "square" is that there are two dimensions in a
square (height and width) and the number being squared appears *twice* in
the calculation. In fact, the term "square" is no coincidence--the square of a
number is the area of the square with sides equal to that number.

A number that is the square of a whole number is called a perfect square.
4^{2} = 16
, so 16 is a perfect square. 25 and 4 are also perfect
squares. We can list the perfect squares in order, starting with
1^{2}
:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...

The cube of a number is that number times itself times itself. 5 cubed,
denoted
5^{3}
, is equal to
5×5×5
, or 125. 2 cubed is
2^{3} = 2×2×2 = 8
. The term "cube" can be remembered
because there are three dimensions in a cube (height, width, and depth)
and the number being cubed appears three times in the calculation.
Similar to the square, the cube of a number is the volume of the cube
with sides equal to that number--this will come in handy in higher levels of math.

The "2" in "
5^{2}
" and the "3" in "
5^{3}
" are called
exponents. An exponent indicates the number of times we must multiply the
base number. To compute
5^{2}
, we multiply 5 two times
(5×5)
, and
to compute
5^{3}
, we multiply 5 three times
(5×5×5)
.

Exponents can be greater than 2 or 3. In fact, an exponent can be any number.
We write an expression such as "
7^{4}
" and say "seven to the fourth
power." Similarly,
5^{9}
is "five to the ninth power," and
11^{56}
is "eleven to the fifty-sixth power."

Since any number times zero is zero, zero to any (positive) power is always
zero. For example,
0^{31} = 0
.

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