## 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 45.
• 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. 25 ÷ 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

(Py)z = Pyz

 Py = Py-z Pz

(PT)y = Py Ty

 1 = P-y Py
 P y = Py T Ty

z√Py = Py/z or (P1/z)y

 P-(y/z) = 1 Py/z

√P = P½

Py x Pz = Py+z

y√P = P1/y