| Isaac Dalby - Mathematics - 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* —... | |
| John Dougall - 1810 - 580 pages
...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,... | |
| Warren Colburn - Algebra - 1828 - 276 pages
...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... | |
| Warren Colburn - Algebra - 1829 - 276 pages
...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.... | |
| Warren Colburn - Algebra - 1830 - 276 pages
...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.... | |
| William Smyth - Algebra - 1830 - 264 pages
...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... | |
| Warren Colburn - Algebra - 1831 - 276 pages
...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... | |
| Warren Colburn - Algebra - 1833 - 276 pages
...= (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.... | |
| Warren Colburn - Algebra - 1834 - 276 pages
...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... | |
| John H. Harney - Algebra - 1840 - 288 pages
...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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