 | Warren Colburn - 1841 - 288 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... | |
 | Warren Colburn - 1844 - 280 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... | |
 | Warren Colburn - 1844 - 280 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... | |
 | Charles Davies - 1845 - 382 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... | |
 | William Smyth - 1851 - 272 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... | |
 | Joseph Ray - 1848 - 250 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... | |
 | Henry Law - 1853 - 84 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... | |
 | Charles Davies, William Guy Peck - 1855 - 628 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... | |
 | William Smyth - 1855 - 370 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... | |
 | Charles Davies - 1857 - 408 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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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... 
