Exponents are the shorthand notation for the repeated multiplication of a single number by itself. For example, if we want to multiply the number 5 by itself 3 times, that is we want to perform the operation 5x5x5, the notation which we would use is 5^3.<\/p>\n
Consider the example: 5x5x5 = 5^3<\/p>\n
In this example, the exponent is 3. The value of the exponent represents how many times the value is being multiplied. So, an exponent of 3 in the expression 5^3 tells us that we want to multiply the value of 5, 3 times. The value which is being multiplied, which in this case is 5, is called the base.<\/p>\n
The process of using exponents is called \u201craising to the power\u201d, where the exponent is the \u201cpower\u201d.<\/p>\n
The expression \u201c5^3\u201d is read as \u201cfive, raised to the third power\u201d or \u201cfive, raised to the power of three\u201d. There are two specially-named powers, \u201cto the second power\u201d is generally pronounced as \u201csquared\u201d and \u201cto the third power\u201d is generally pronounced as \u201ccubed\u201d. So \u201c5^3\u201d would commonly be pronounced as \u201cfive cubed\u201d.<\/p>\n
When we deal with numbers, we typically simplify the expression because it is generally easier to deal with \u201c27\u201d than to deal with \u201c3^3\u201d.<\/p>\n
However, when we are dealing with variables, we need the exponents because it is easier to deal with the expression \u201cx^6\u201d than \u201cxxxxxx\u201d.<\/p>\n
Here are some more examples:<\/p>\n
4x4x4x4 = 4^4<\/p>\n
3x3x3 = 3^3<\/p>\n
2x2x2x2x2 = 2^5<\/p>\n
3x3x3x3 = 3^4<\/p>\n
5×5 = 5^2<\/p>\n