### 4. Powers of integers

If *a * is an integer, the product of *a * for *n* times is denoted by .

*a ^{n} = a · a · …n times….a*

*a * is called the **base, the repeated factor**,

*n * is called the **index**, the times a is repeated

*a ^{n} *and itself is called the nth power of

*a*.

**4.1. Sign of the power of an integer**

This is a difficult point for you.

If the exponent is a natural number:

- If the base is positive, the power is positive.
- If the base is negative, the power is positive if the exponent is an even number and negative if the exponent is an odd number.

**4.2. Properties of Powers**

These are the properties of powers. You **must** learn them by heart.

**1. a ^{0} = 1 **

**2. a ^{1} = a**

**3. a ^{n} · a^{m} = a^{n+m } **

**4. a ^{n}:· a^{m} =a^{n-m}**

**6. (a ^{n})^{m} = a^{n·m}**

**7. (a : b) ^{n}= a^{n}: b^{n }**

**8. (a · b) ^{n}= a^{n}· b^{n}**

You can practice in

**http://descartes.cnice.mec.es/materiales_didacticos/ing_potencias/index.htm**

** **but the bases are natural numbers, and on the web

**http://www.kwiznet.com/p/takeQuiz.php?ChapterID=2169&CurriculumID=22**

On this web you have to click on ABCD. Some of the questions are not avalaible if you don’t pay (IT IS NOT NECESSARY !!!)

** **

### 5. Combined operations

Combined operations are probably the more complicate point on calculations. Remember the order of operations. When you are computing do:

- What is inside the brackets and square brackets.
- Powers and roots.
- Multiplication and division from left to right.
- Addition and subtraction from left to right.

Practise on the links bellow

**All types from Difficulty Level 1**** Elemental level**

**All types from Difficulty Level 2**** Easy level**

**All types from Difficulty Level 3**** Required level**

**All types from Difficulty Level 4**** Higher level**

Finally here you are a video on combined operations, very useful

### 6. Word problems with integers

Word problems with integers require a good understanding of the cocept of integer number as well as a comprehesion of the statement. Read it three times at least.

Practise on the bellow links

http://www.ixl.com/math/practice/grade-8-add-and-subtract-integers-word-problems

In this link, you will find not only the solutions but also the explanations.

http://www.mathgoodies.com/lessons/vol5/challenge_vol5.html

These problems have a higher level. They can have hints but no explanation.