Product (mathematics)

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In mathematics, a product is a number or a quantity obtained by multiplying two or more numbers together. For example: 4 × 7 = 28 Here, the number 28 is called the product of 4 and 7. The product of 6 and 4 will be 24, because 6 × 4 = 24.

Capital pi[change | change source]

A short notation for long multiplication expressions is the product notation. It uses the capital Greek letter pi: . This works the same as the Sigma notation.

Properties[change | change source]

(n! means n factorial)
because we multiply n by itself n times.
where c is a constant.

From the above equation we can see that any number with an exponent can be represented by a product, though it normally is not desirable.

Unlike summation, the sums of two terms cannot be separated into different sums. That is,


This can be thought of in terms of polynomials: you normally cannot separate terms inside them before they are raised to an exponent!

Relation to Summation[change | change source]

The product of powers with the same base can be written as an exponential of the sum of the powers' exponents: