and multiplicand. For example, what is 3200 × 3000? First, 3200 is 32 × 100, or one hundred times as great as 32. Again, 32 × 13000 is 32 × 13, with three ciphers affixed, that is 416, with three ciphers affixed, or 416000. But the product required must be 100 times as great as this, or must have two ciphers affixed. It is therefore 41600000, having as many ciphers as are in both multiplier and
- When any number is multiplied by itself any number of times, the result is called a power of that number. Thus:
| 6 is called the | first power | of 6 |
|---|---|---|
| 6 × 6 | second power | of 6 |
| 6 × 6 × 6 | third power | of 6 |
| 6 × 6 × 6 × 6 | fourth power | of 6 |
| &c. | &c. |
The second and third powers are usually called the square and cube, which are incorrect names, derived from certain connexions of the second and third power with the square and cube in geometry. As exercises in multiplication, the following powers are to be found.
| Number proposed. | Square. | Cube. |
|---|---|---|
| 972 | 944784 | 918330048 |
| 1008 | 1016064 | 1024192512 |
| 3142 | 9872164 | 31018339288 |
| 3163 | 10004569 | 31644451747 |
| 5555 | 30858025 | 171416328875 |
| 6789 | 46090521 | 312908547069 |
| The fifth | power of 36 is | 60466176 |
| fourth | 50 | 6250000 |
| fourth | 108 | 136048896 |
| fourth | 277 | 5887339441 |
It is required to multiply a + b by c + d , that is, to take a + b as many times as there are