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Squares, Cubes, 4th powers, and 5th powers. Term. 1 / 45. 1 squared. Click the card to flip 👆. Definition.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.
Exponents. The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".
There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "5 3" is commonly pronounced as "five cubed". When we deal with numbers, we usually just simplify; we'd rather deal with "27" than with "3 3".
Squares. The square of a number is that number times itself. 5 squared, denoted 52, is equal to 5×5, or 25. 2 squared is 22 = 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.
When the exponent is \(2\), the result is called a square. When the exponent is \(3\), the result is called a cube. Memorize the squares of the integers up to \(15\) and the cubes of the integers up to \(10\). They will be used often as you progress in your study of algebra.
