Mathematics in Business and Economics
Indices or Powers
Indices or powers show how many times a number is multiplied by itself. 13³ means 13 x 13 x 13.
The rules
- To multiply numbers with different powers (for example, 4² x 4³) simply add the powers together - the answer in this case is 4^{5}.
- Any number to the power of 0 = 1.
- Negative powers require us to understand the relationship between multiplying and dividing. A negative power, for example, 2^{-3} is the same as ½³.
- When dividing same numbers with powers, subtract the powers, e.g. 2^{5} ÷ 2² = 2³.
- If multiplying same numbers with a mix of positive and negative powers, add together the powers.
- With powers of negative numbers, (-5)² = -5 x -5. A minus times a minus gives a plus and 5 x 5 = 25. The answer therefore is 25.
- Negative numbers raised to odd powers (such as (-2)^{3}) will have a negative sign. Again this is because of the rule of multiplying positive and negative numbers. (-2)^{3} = -2 x -2 x -2 which is a negative number times a negative number (-2 x -2 = 4) and then this multiplied by another negative number (4 x -2). So the answer is -8.
Summary of the Rules
(P^{y})^{z} = P^{yz}
P^{y} | = P^{y-z} |
P^{z} |
(PT)^{y} = P^{y} T^{y}
1 | = P^{-y} |
P^{y} |
P | ^{y} | = | P^{y} | ||
T | T^{y} |
^{z}√P^{y} = P^{y/z} or (P^{1/z})^{y}
P^{-(y/z)} = | 1 |
P^{y/z} |
√P = P^{½}
P^{y} x P^{z} = P^{y+z}
^{y}√P = P^{1/y}