Exponents
There's one more operation besides addition, subtraction, multiplication, and division. That's exponentiation, notated by superscript (e.g.or), or sometimes -- especially on calculators and computers -- using the symbol ^.
means "to the power", or in other words:
. (Remember, it's not just.) Theis thebaseand theis theexponent. This is also called "squared"; it's the area of a square of side. (Seesquare roots.)
The exponent tells you how many times to use the base as a factor. In the example below, the base isand the exponent is, so we find the product of four threes.
.
Example:
Which is greater,or?
Answer:
, while
.
To answer the question,is greater.
To simplify more complicated expressions, see the page onproperties of exponents. This page also deals with negative and rational exponents.
Some good sequences to remember (they come up in mathematics all the time) are the square numbers and the powers of two:
Powers of
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Square Numbers
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Clickherefor more stuff aboutexponent tables and patterns.
One important use of exponents is to express really large (or really small) numbers: this is calledscientific notationand uses powers of ten.
Examples:
and