...or any quantity which, multiplied by the divisor a3, will equal the dividend a5, must be aa, or a2. Hence, The EXPONENT of a letter in the quotient is...dividend, diminished by its exponent in the divisor. 2. Let it be required to divide a" by a". Then, ~n = a"-" = a°; but ~n = 1. Therefore (Ax. 7), a°...

...xy, is the same as axy •*- a, which is equal to xy ; for xy xa = axy. 3. The exponent of a factor in the quotient is equal to its exponent in the dividend diminished by its exponent in the divisor. Thus, a5 -*- a2, or a5 with the factor a2 omitted, is equal to a3, for a* xa* = a5. 4. The quotient...

...dividend a factor equal to the divisor, might have been obtained at once, by taking the difference of the exponents, 5 and 3. Hence, The exponent of...is the exponent of a letter in the quotient equal ? 70i When the exponents of the same letter in the dividend and divisor are equal, the letter may be...

...dividend a factor equal to the divisor, might have been obtained at once, by taking the difference of the exponents, 5 and 3. Hence, The exponent of...division what do like signs produce ? Unlike signs ? How manv cases in division of algebraic quantities ? Explain the first operation un, dcr Case I. The second....

...required must be such a quantity as when multiplied by a3 will produce a3. That quantity is evidently a2. Hence, The exponent of a letter in the quotient is...dividend diminished by its exponent in the divisor. Or, in general, am -=- a" = am~n. 94. If we apply the rule of Art. 93 to finding the quotient of am...

...a quantity as when multiplied by «3 \vill produce a6. That quantity is evidently a'2. Hence, T/ie exponent of a letter in the quotient is equal to its...dividend diminished by its exponent in. the divisor. Or, in general, am -;- a" = am~n. 94. If we apply the rule of Art. 93 to finding the quotient of a"'...

...to t1ie coefficient of ike dividend divided by t1iat of the divisor. 3. The exponent of any quantity in the quotient is equal to its exponent in the dividend diminished by its exponent in t1ie divisor. 89. The principle relating to the signs in division may be illustrated as follows: +...

...quantity which, when multiplied by «3, will produce cf. That quantity is evidently a? ; hence That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. For example, — = ara~". a" DIVISION OF MONOMIALS. 90. We derive...

...multiplied by a3, will produce cf. That quantity is evidently a2 ; hence a5 « — = a2. a3 That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. am For example, — = a"-*, a" DIVISION OF MONOMIALS. 90. We derive...

...quantity which, when multiplied by will produce as. That quantity is evidently a2 ; hence That is, the exponent of a letter in the quotient is equal to its exponent in the dividend minus its exponent in the divisor. For example, — = a*~". DIVISION OF MONOMIALS. 90. We derive from...