...required. Thus a 3 raised to the third power Conversely to extract the root of a simple quantity, we divide the exponent of each letter by the index of the root. Thus The utility of exponents of the kind, which we are here considering, consists principally in this,...

...of a simple quantity to any degree whatever, we must (1.) extract the root of the coefficient, (2.) divide the exponent of each letter by the index of the root. Thus, 3 4 ^/64an3~c6 = 4a36c2; ^/l6«s6i2^ — 2a26*c. We see, according to this rule, that in order...

...Extraction of Roots. 199. To extract the n" root of a monomial, follow the rule given in Art. 182, viz. divide the exponent of each letter by the index of the root. For, the exponent of each letter in the result should be such, that multiplied by n, the index of the...

...Involve a * to the y power. ii t» vr a" ' = EXTRACTION OF ROOTS. RULE. (68.) Extract the root of the coefficient, and divide the exponent of each letter by the index of the required root. t. 2 1 Thus, the square root of a3 is or; and the cube root of a? is a* * = a* . EXAMPLES....

...Hence, reciprocally, to extract any root of a monomial, 1st. Extract the root of the co-efficient. 2d. Divide the exponent of each letter by the index of the root. V64a 9 2rV=4a 3 Ac 3 ; Vl6a 8 i l V=2a 3 i 3 c. From this rule, we perceive, that in order that a monomial...

...power, and unite the terms. Hence, to extract any root of a monomial, 1st. Extract the root of the co-efficient and divide the exponent of each letter by the index of the root. 2d. To the root of the coefficient annex each letter with its new exponent, and the result will be...

...following RULE. For the extraction of the roots of monomials. Extract the root of the numeral 'coefficients and divide the exponent of each letter by the index of the root. EXAMPLES. 1. What is the square root of 49a3x4? Ans. lax3. 2. What is the square root of 25c'663? Ans.5csb....

...factors. Thus the cube root of 8x2 is 2x. RULE . — Extract the root of the numeral coefficients, and divide the exponent of each letter by the index of the root. EXAMPLES. 1. What is the second root of 9o2aV ? , . Ans. 3aary. 2. What is the third root of 8aV ?...

...following RULE. For the extraction of the roots of monomials. Extract the root of the numeral coefficients and divide the exponent of each letter by the index of the root. EXAMPLES. 1. What is the square root of 49a?x t ? Ans. 7aaf. 2. What is the square root of 25e I0 6...

...power required. _2 Thus a raised to the third power Conversely, to extract the root of a monomial, we divide the exponent of each letter by the index of the root. Thus tfa-3 = a~3. The utility of exponents, of the kind which we are here considering, consists principally...