Powers and Roots
Powers
52 is read five squared or five to the power of two. It equals 5 × 5 = 25.
53 is read five cubed or five to the power of three. It equals 5 × 5 × 5 = 125.
54 is read five to the power of four. It equals 5 × 5 × 5 × 5 = 625.
Powers or exponents are used to write down in a short way the multiplication of a number with itself, over and over again. 510 is five to the power of ten. Without using the "power" notation, the multiplication is
5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5. Even when this example is written as a single number, 9765625, it is more to write than when the power notation is used. Mathematical notation is often used to write things down in a short way. Don't let notation confuse you - it is there to make your life easier. Power notation can be used to write very large or very small numbers in a standard form.
The power notation can also be used with letters.
Powers and algebra
Everything that has been said above for the number 5 could also be said for x, or any other letter. For example x3 means x cubed or x to the power of three. See also the notes on substitution.
If x = 5 then x3 = 125
If x = 2 then x3 = 8
If x = 10 then x3 = 1000
Roots
Roots are the opposite of powers. The square root of 25 is the number which you must square to get 25. The square root of 25 is 5. Using notation (√ is the sign for square root):
√25 = 5 Alternatively this may be written:
Square roots occur often in mathematics, but there are other roots. The cube root of 25 and the fourth root of 25 are the numbers that, when cubed or raised to the power of 4 give 25.
If the root of a number is not a whole number it is unlikely that you will be able to find it without a calculator. Answers that are not whole numbers should be rounded appropriately. Normally 3 significant figures is sufficient.
3√25 = 2.92 (to 3 significant figures)
4√25 = 2.24 (to 3 significant figures)