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" Powers of the same quantity are divided by subtracting the exponent of the divisor from that of the dividend ; the remainder is the exponent of the quotient. "
Elements of Algebra - Page 196
by William Smyth - 1833 - 280 pages
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The Tutor's Guide: Being a Complete System of Arithmetic; with Various ...

Charles Vyse - Arithmetic - 1806 - 342 pages
...Letters, and proceed as in Sect. V. ,5. Different Powers or Roots of the same Quantity are divided by subtracting the Exponent of the Divisor from that of the Dividend, and placing the Remainder as an Ex_._ponent to the Quantity given. EXAMPLES. Divisor. Dividend. (1)...
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The Tutor's Guide: Being a Complete System of Arithmetic; with Various ...

Charles Vyse - Arithmetic - 1815 - 340 pages
...its letters, and proceed as in Sect. 5. 5. Different powers or roots of the same quantity are divided by subtracting the exponent of the divisor from that o'F the dividend, and placing the remainder as an exponent to the quantity given. EXAMPLES. Divisor. Dividend. d)ad+6d(...
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A Treatise of Algebra: Wherein the Principles are Demonstrated ... To which ...

Thomas Simpson - Algebra - 1821 - 426 pages
...2cy is 36 \/ Sax. 5°. Different powers, or roots of the same quantity are droided one by another, by subtracting the exponent of the divisor from that of the dividend, and placing the remainder as an exponent to the ipumlitij given. But it must be observed, that the...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1825 - 400 pages
...Negative Exponents. It was observed above, that when the dividend and the divisor were different powers of the same letter, division is performed by subtracting...exponent of the divisor from that of the dividend : thus Now - = 1. By the above principle -=aI-1=o°; therefore o° = 1. Also -=- = a3"3 = a° = 1 ;...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1826 - 290 pages
...different, to numbers. Multiplication, we observed, is performed by adding the exponents, and division by subtracting the exponent of the divisor from that of the dividend. Thus o3 X «' is o3*6 = a8. And — is a'-" = a'. a In the same manner 23 X 26 = 28+J = 2s, and —t...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1828 - 330 pages
...Negative Exponents. It was observed above, that when the dividend and the divisor were different powers of the same letter, division is performed by subtracting...exponent of the divisor from that of the dividend : thus Now £ = 1 . By the above principle - = «'~' = a° ; therere a fore a° = 1 . Also £. = a3-3...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...of the quotient is + ; but if they be unlike, it is — .* Powers of the same quantity are divided by subtracting the exponent of the divisor from that of the dividend ; the remainder is the exponent of the quotient. If the dividend be compound, divide each term of it separately...
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Library of Useful Knowledge: Mathematics I.

Mathematics - 1836 - 352 pages
...second rule in art. [230], the exponent of the quotient of two powers of the same quantity is found by subtracting the exponent of the divisor from that of the dividend. The logarithm of a quotient is therefore the difference of the logarithms of the dividend and divisor....
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 320 pages
...numerator. This fraction, reduced to its lowest terms, becomes -; but if the division represented, be performed by subtracting the exponent of the divisor from that of the dividend, the fraction becomes a1"2 = a~ l. These two values of the fraction must be equal, and hence, - = a-1. Again,...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 314 pages
...of the same quantity are multiplied together by adding the exponents, and divided one by the other by subtracting the exponent of the divisor from that of the dividend ; also, that any power of a quantity is found by multiplying the exponent, and any root is found by...
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