OPERATION. Since a^ =a a a a a, and (f^aaa,

J. it is evident that the quotient, or the

— = (1? quantity which, multiplied by the di-

«' visor c?, will equal the dividend o',

must be a a,, or a'. The exponent 2,

in the quotient, which is the result of rejecting from the dividend

a factor equal to the divisor j might have "been obtained at once,

by taking the difference of the exponents, 5 and a^ Hencp,

THe exponent of a letter in the quotient is equal to its exponent
in the dividend, diminished ly its exponent in the divisor-.
In division what do like signs produce ? Unlilse signs 1 How many
cases in division of algebraic quantities? Explain the first operation un-
der Case I. The second. To what is the exponent of a letter in the
quotient equal?



DIVISION. 47

70. When the exponents of the same letter in the div
idend and diyisor are equal, the letter may be introduced
into the quotient, without affecting the value of the ex-
pression, by writing the letter with the exponent 0.
For, let o" be any power of the quantity a, then, dividing a" by
a", -we have

a« a"

5T = «"-" = <">; but— = 1.
Therefore (Ax. 7), a" c= 1 ; and as a may have any value what-
ever,

Anff quantity whose exponent is is equal to 1.
Hence, by this notation the trace of a letter which
has disappeared in an operation may be preserved, since
the introduction of any factor whose value is unity will
not affect the value of an expression.
Thus, a° b has the same value as b alone.
