 A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.  The elements of algebra - Page 9by Archibald Montgomerie - 1857 - 95 pagesFull view - About this book
 | Geography - 1867 - 878 pages
...(y*)*. And the quotient is (i3)" =«•=*'. Ant. A root ie divideday another not of the same letter or quantity, by subtracting the index of the divisor from that of the dividend. EXAMPL E. — Thus а* -г- a° = a * = •* "• = <** = a • X a*, and this divided by o* U For... | |
 | Isaac Dalby - Mathematics - 1806 - 526 pages
...the surds have coefficients their quotient must bt prefixed. And the quotient of like surds is found by subtracting the index of the divisor from that of the dividend. (49). 5. Divide 8i/10 by C. Divide J t/£ by 7. Divide a y'i by c \/ d\ a , ^ , — - V 'Ac Y d xz... | |
 | William Nicholson - Natural history - 1809 - 716 pages
...then by ft, the .aftc , be result will be the same ; for — = Ac, and — =c, as "before. Hence, any power of a quantity is divided by any other power...quantity, by subtracting the index of the divisor from the index of the dividend. vidend as the case may require, and repeat the operation till all the terms... | |
 | Jeremiah Day - Algebra - 1814 - 304 pages
...Divide i \m By i/3x Jdx aa (ax)v .Quot. 286. A root is divided by another root of the some, letter or quantity, by subtracting the index of the divisor from that of the dividend. l II l 3 i J i Thus a*-:- a* = a* * = ai * = a* = a*. * ' For a* = 0s = a? xa*' xa* and this divided... | |
 | James Wood - Algebra - 1815 - 338 pages
...then by b, the result will be the same; for - = bc, and -j-= c, as before. ab (84.) COR. Hence, any power of a quantity is divided by any other power of the same quantity, by taking the index of the divisor from the index of the dividend. a? Thus, ~ = a* ; ~ =r = a-3 (Art.... | |
 | John Bonnycastle - Algebra - 1818 - 284 pages
...products (e). '• It it here also to he observed, that powers and roots of the same quantity, are divided by subtracting the index. of the divisor from that of the dividend. Thus, a3-4-aa, or — = o ; a^-^-a3, or, ^\ = a? ; a* n? ^-x3 or — — a** ,, andam-i<iB or ^=om—n.... | |
 | William Nicholson - Arts - 1819 - 432 pages
...result will be the same; for = d c, and — =c, as before. Hence, any power of a quantity is dividedby any other power of the same quantity, by subtracting the index of the divisor from the index of the dividend. Thus, - =0';-,= — =0—s ; =fpn—aa) ai a? a" If only a part of the product... | |
 | Jeremiah Day - Algebra - 1820 - 352 pages
...=~-=«*. And am-r-<f=Jr=am-". Hence, 237. A POWER MAY BE DIVIDED BY ANOTHER POWER OF THE SAME ROOT, BY SUBTRACTING THE INDEX OF THE DIVISOR FROM THAT OF THE DIVIDEND. By -3a3 2&3 a' Quot. — 3y4 b + 3y4 yyy Thus y *-ry* •=*?-2 »/'. That is— =i/. aa" And a"+'--'0=«"+iI=«".... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...or to a . a, a .a .a .a or to a5; the division of different powers of the same quantity, is effected by subtracting the index of the divisor from that of the dividend. ALGEBRAICAL CALCULATION. EXAMPLES IN DIVISION 1. Divide б a by 2. Answer, 3 a. 2. Divide 7 ab by a.... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...products*. It is here also to be observed, that powers and roots of the same quantity, are divided by subtracting the index of the divisor from that of the dividend. "3 T 4 <4 -1 Thus, a3-r-a1, or— ;=a; a -~a , or,— =e» ; a oj 3 % . •? or_=aT* ; and am-7-on,... | |
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