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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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An Introduction to Algebra, Upon the Inductive Method of Instruction

Warren Colburn - 1841 - 276 σελίδες
...is already a power of a compound quantity, may be raised to any power by multiplying its exponent oy the exponent of the power to which it is to be raised. 1. Express the 2d power of (3 b — c)4. 8. Express the 3d power of (a — c + 2 d)°. 9. Express the...

An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1844 - 276 σελίδες
...ft)*' = (a + 6)'. The 3d power of (2 a — d)4 is (2a— d)*H+« = (2a — <f)'*' = (2a — </)"• That is, any quantity, which is already a power of...(3 b — c)4. 8. Express the 3d power of (a — c -f- 2 rf)5. 9. Express the 7th power of (2 a* — 4 c3)*. Division may also be performed by subtracting...

An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1844 - 276 σελίδες
...until it is taken as many times as there are units in the exponent of the required power. Hence any quantity may be raised to any power by multiplying...exponent of the power to which it is to be raised. The 5th power of a3 is a3*6 = a". The 3d power of a7 is a7*3 = a", <fcc. The power of a product is...

Elements of Algebra: Including Sturms' Theorem

Charles Davies - 1845 - 368 σελίδες
...to square y3b, we have y36 = \f^/3b: hence, Consequently, 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. Let it be required to...

Elementary Algebra: For the Use of Schools

William Smyth - 1851 - 236 σελίδες
...a number, therefore, to a power, by means of logarithms, we multiply the logarithm of the proposed 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. Again, let it be...

Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - 1848 - 240 σελίδες
...we may obtain any power of a quantity by taking it as a factor as many times at there are units in the exponent of the power to which it is to be raised. This rule alono, is sufficient for every question in the formation of powers ; but, for the more easy...

Rudimentary Treatise on Logarithms

Henry Law - 1853 - 68 σελίδες
...af -=-*"• = *<" - "•>. 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 xm is x"-m. 4. The extraction of the root of any power is performed by...

Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 592 σελίδες
...this in the given equation, we have 2 :в, 3 21 X 2'' = 6 ; whence, 3\«' _| _ o ÍQ\ 2 1 -2....W. A quantity may be raised to any power by multiplying its exponent by the exponent of the power : thus, (a -»)-• = tt«r. Any root of a quantity may be extracted by dividing the exponent by the...

Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - 1855 - 336 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 it be...

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

Charles Davies - 1857 - 400 σελίδες
...Again, to square 1/36, we have */36 = \\'- hence, /36; 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...




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