Exponent Rules

WARNING!!! Do NOT memorize these -- they easily get jumbled!!

Test makers know that students can easily mix these up!!
Encouraging students to write it out is the most useful!
(x^2)^3 = (x)(x) three times = (x)(x)(x)(x)(x)(x) = x^6!!

Divisbility Rules

The most important one is 3. If the digits in a number add up to 3 or a multiple of 3, then the number is divisible by 3. Some examples include 12, 51, 57, 111, 666, 1113.

If the number is divisible by 9, then the digits will add up to 9 or a multiple of 9. Plus if it is divisible by 9, then it must be divisible by 3 as 9 is composed of 3 x 3. Examples include 27, 333, 981, 1836, 111111111.

If the number is divisible by 3 and is even, then 3 and 2 must be factors and therefore the number is divisible by 6. Some examples include 666, 1836, 222, 3300.

Two Negatives Make a Positive -- I Don't Not Like Pizza

8 - - 12 = 8 + 12 = 20

8 - 12 = -4

Using a number line to illustrate these concepts is very helpful. Only put a few numbers on a number line -- include 0 and wherever the beginning point is (in this case 8). Then consider if your answer is more positive or negative than your beginning point (in this case 8).


The Negative Sign is the Most Common Mistake in Math!!

Either there is one too many negative or one too few. Check work carefully as this can be tricky -- expect to find mistakes!!

Also, the comparative can help tremendously here: -6 + 6 can not equal -6 + -6!!