Order of Operations - Special Cases

Special Cases

An exclamation mark indicates that one should compute the factorial of the term immediately to its left, before computing any of the lower-precedence operations, unless grouping symbols dictate otherwise. But 23! means (23)! = 8! = 40320 while 23! = 26 = 64; a factorial in an exponent applies to the exponent, while a factorial not in the exponent applies to the entire power.

If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:

Sometimes a heavy dot is used as a multiplication sign which indicates that the entire expression before the heavy dot is multiplied by the entire expression after the heavy dot, but this notation may be misunderstood. Thus x + y • a + b may be used for (x + y)(a + b), but the latter notation is more common.

Read more about this topic:  Order Of Operations

Famous quotes containing the words special and/or cases:

    With a generous endowment of motherhood provided by legislation, with all laws against voluntary motherhood and education in its methods repealed, with the feminist ideal of education accepted in home and school, and with all special barriers removed in every field of human activity, there is no reason why woman should not become almost a human thing. It will be time enough then to consider whether she has a soul.
    Crystal Eastman (1881–1928)

    We noticed several other sandy tracts in our voyage; and the course of the Merrimack can be traced from the nearest mountain by its yellow sand-banks, though the river itself is for the most part invisible. Lawsuits, as we hear, have in some cases grown out of these causes. Railroads have been made through certain irritable districts, breaking their sod, and so have set the sand to blowing, till it has converted fertile farms into deserts, and the company has had to pay the damages.
    Henry David Thoreau (1817–1862)