Exponent notation
When the same number is multiplied by itself over and over, how do you write it short, and which of these powers are worth knowing by heart?
Where you are 3 inside
What this area is about
An exponent is shorthand for repeated multiplication. In 3^4 the base 3 is the factor and the exponent 4 counts how many times it appears, so 3^4 = 3 \times 3 \times 3 \times 3 = 81. The notation keeps long products short, and a few families of powers turn up so often that they are worth recognizing on sight.
How these fit together
The notation. Base, exponent and the value of a power names the parts of a power and works out what it equals.
Powers worth knowing. Perfect squares and perfect cubes are numbers such as 49 = 7^2 and 27 = 3^3, which can be laid out as a full square or stacked as a full cube. Powers of ten such as 10^3 = 1{,}000 are what each place value column is worth.
A path through it
Start with base and exponent. Perfect squares and cubes come after it; powers of ten can come before or after them.
Next, the order of operations with powers says when a power is worked out, the laws of exponents calculate with powers without unpacking them, and square roots undo squaring.