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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 Course of Mathematics ...: Designed for the Use of the Officers ..., Τόμος 2

Isaac Dalby - 1806
...difference. Of involving Surds: And extracting their Roots. 124. SURDS are involved by multiplying the index by the exponent of the power to which it is to be raised. (100). Thus, the cube of a? is aj X 3 = a*. And the square of (a*— x*)2 is (a*— x*)^ X 2 = a* —...

The Modern Preceptor Or a General Course of Education: Containing ..., Τόμος 1

John Dougall - 1810 - 580 σελίδες
...in the question. Involution of Roots is performed by multiplying the logarithm of the given number by the exponent of the power to which it is to be raised, when the product will be the logarithm of the power required. For example, rajse 8 to the 2nd power,...

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1828 - 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 its exponent by ike exponent of the power to which it is to be raised. The 5th power of a3 is a3X5 = a". The 3d power...

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1829 - 276 σελίδες
...The 3d power of (2 a — </)4 is (2a — rf)'+4+» = (2« — J)'x3:=(2a — rf)13. That is, «»i/ quantity, which is already a power of a compound quantity,...be raised to any power by multiplying its exponent oy the exponent of the power to which it is to be raised. 7. Express the 2d power of (36 — c)4. 8....

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1830 - 276 σελίδες
...of (2 a — d)4 is (2« — rf)4+4+1 = (2a — rf)4x3 = (2a — rf)''. That is, any quantity, whkh is already a power of a compound Quantity, may be raised to any power by multiplying its exponent y the exponent of the power to which it is to be raised. 7. Express the 2d power of (3 b — c)4. 8....

Elements of Algebra

William Smyth - 1830 - 264 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. Again let it be...

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1831 - 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 its exponent by the exponent of the poiver to which it is to be 'raised. • The 5th power of a3 is a3*5 == a15. The 3d power of a7 is...

An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1833 - 276 σελίδες
...= (a + 6)3** = (a + b)<. The 3d power of (2 a — rf)4 is (2« — </)'+<+' = (2a — d)*x3=(2a — d)". That is, any quantity, which is already a power...is to be raised.. 7. Express the 2d power of (3 b — c)'. 8. Express the 3d power of (a — c + 2 dy. 9. Express the 7th power of (2 a5 — 4 c3)3....

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1834 - 276 σελίδες
...X (« + by - (a +b)*> =(a + 6)'xi = ( The 3d power of (2 a — d)f is (2a— d)4+'+4 = (2a — d)4 That is, any quantity, which is already a power of...(3 b — c)4. 8. Express the 3d power of (a — c + 2 d)'. 9. Express the 7th power of (2 a' — 4 c')'. Division may also be performed by subtracting...

An Algebra Upon the Inductive Method of Instruction

John Hopkins Harney - 1840 - 288 σελίδες
...third power of a, or the third power of the second root of a. As we can raise any power of a to a given power, by multiplying its exponent by the exponent of the power to which it is to be raised, we may obtain the root of any power by dividing the exponent of the power. Thus, the second root of...




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