Contents:

• Powers:
• Roots:
• Summary of Rules:

Powers: 3where 3 is the base and is the index of exponent.

A number multiplied by itself is its square ie. 3 x 3 is the same as 3 which equals 9. A number may be multiplied by itself more than twice, that number is the power. ie. 3x3x3x3x3x3 is the same as 3 to power 6 or 3 which equals 729.

Negative powers operate in a similar way but the answer is a denominator with 1 over. ie 3 to power -6 or 3 whichis the same as 13.

The rules for powers when adding or subtracting are different from multiplying or dividing. Care must be taken.

Example: Addition or subtraction: 3+ 3 = 9 + 9 = 18. It is not 6nor 3which give completly different answers.

Example: Multiplication: only when the bases are the same, add the powers. 3x 3= 3 (9 x 9 = 81).

Example: Division: only when the bases are the same, subtract the powers. 3 3 = 3 (7299 = 81).

---

Top of PageTop of Powers

---

Roots: The opposite operation to 3= 9, is equal to9 = 3 is equal to 9.

When dealing with algebraic factors and terms it is simpler to convert a root into a power.

Example: 256 is the 4th root of 256, changing to a power is 256. 4 x 4 x 4 x 4 = 256. 4= 256. Therefore 256 = 4.

---

Top of Page

---

Summary of Rules:

1. Multiplication: When bases are the same add the powers.

2. Division: When bases are the same subtract the powers.

3. Power to a power: (3), multiply the powers; = 3.

4. Base to power zero is equal to 1. The division rule may result in a power zero.

5. Base to a minus power is equal to 1 / base to power.

6.Base to 1/power: the power becomes the value of the root of the base.

---

Top of Page

©Mathstutor.com  2001-2005