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" The 3d power of (2 a — rf)4 is (2a — rf)^«+« = (2a — d)4x3=(2a — d)". That is, any quantity, which is already a power of a compound quantity, may be raised to any power by multiplying its exponent by the exponent of the power to which it is... "
An Introduction to Algebra: Upon the Inductive Method of Instruction - Σελίδα 186
των Warren Colburn - 1837 - 276 σελίδες
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A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - 1858 - 320 σελίδες
...number by means of a table of logarithms, we multiply, therefore, the logarithm of the proposed number by the exponent of the power, to which it is to be raised; the number in the table corresponding to this product, will be the power sought. " • 4. Again, let...

Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ...

Charles Davies, William Guy Peck - 1859 - 592 σελίδες
...a* — a*+iOne may be divided by the other by subtractin" their exponents: thus, A quantity may he raised to any power by multiplying its exponent by the exponent of the power : thus, (a -»)-• = л'». Any root of a quantity may be extracted by dividing the exponent by the...

Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 σελίδες
...gives Again, to square *f3b, we have *f3b = \J \f"3b- hence, When the index of the radical is divisible by the exponent of the power to which it is to be raised, perform the division, leaving the quantity under the radical sign unchanged. Extraction of Roots of...

Arithmetical examples for military and civil service students

William Alfred Browne - 1863
...example, 54-f-52= (5 x 5 x 5 x 5) -5- (5 x 5 = 52. 828. A power of any number is raised to any other given power by multiplying its exponent by the exponent of the power to which it is to be raised. For example (42)2 (which means that 4 is to be raised to the second power,) = 42 x 45=44. OS iH CO...

New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - 1863 - 420 σελίδες
...exponents. To explain the origin of this method of indicating roots, we observe that a quantity is raised to any power, by multiplying its exponent by the exponent of the required power. Conversely, any root of a quantity may be obtained, by dividing the exponent of the...

New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - 1864 - 420 σελίδες
...exponents. To explain the origin of this method of indicating roots, we observe that a quantity is raised to any power, by multiplying its exponent by the exponent of the required power. Conversely, any root of a quantity may be obtained, by dividing the exponent of the...

Mathematical Tables Consisting of Logarithms of Numbers 1 to 108000 ...

James Pryde - 1878 - 454 σελίδες
...result as before. ( 15 ) To PERFORM INVOLUTION nr LOGARITHMS. Multiply the logarithm of the given number by the exponent of the power to which it is to be raised, and the product will be the logarithm of the required power. » EXAMPLE. Find the cube of 307146. L...

Mathematical tables

James Pryde - 1878
...result as before. ( 16 ) To PERFORM INVOLUTION RY LOGARITHM8. Multiply the logarithm of the given number by the exponent of the power to which it is to be raised, and the product will be the logarithm of the required power. EXAMPLE. Find the cube of 30-7146. L 30-7146...

The Inductive Algebra: Embracing a Complete Course for Schools and Academies

William James Milne - 1881 - 347 σελίδες
...the root. For, since in raising a quantity to a given power we multiply the exponent of the quantity by the exponent of the power to which it is to be raised, in finding a root the exponent of the quantity should be divided by the index of the root. fl *..„..,...

Mathematical tables for trigonometrical, astronomical, and nautical ...

Henry Law - 1884
...is, «" -r- xm = «<" ~ "'>. 3. The involution of any power of a quantity to some power is performed by multiplying its exponent by the exponent of the power to which it is to be raised ; that is, the nth power of af"ie,xn-'". 4. The extraction of the root of any power is performed by...




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