Math Tip of the Day: Integers and Exponents

Understanding integers is one of the hardest things for some students to accomplish.  Positives and negatives.  Who wants to deal with that?  Master integers with these tips.

Applying exponents are a way of doing extended multiplication.  Which isn’t really that bad.  But when integers and exponents are combined, things can get tricky.  But don’t stress, it is achievable.

Integers and Exponents

1.  When an exponent is an even number and there is a negative involved, the answer will almost always be positive.

Example:  32 = 3 x 3 = 9

(3)2 = 3 x 3 = 9 

(-3)2 = -3 x -3 = 9.  This answer is also positive because a negative times a negative equals a positive.

Exception to the rule:  -32 = 3 x 3 = 9.  When the negative is applied, the answer is negative.  So therefore, the answer is -9.

**You must apply the exponent first, and then apply the negative because of order of operations.

 

2.  When an exponent is an odd number and there is a negative involved, the answer will almost always be negative.

Example:  (-2)3 = -2 x -2 x -2 = -8.  A negative times a negative is a positive.  Then a positive times a negative is a negative.

-23 = 2 x 2 x 2 = 8. When the negative is applied, the answer is negative.  So therefore, the answer is -8.

Exception to the rule:  -(-2)3 = -2 x -2 x -2 = -8.  When the negative is applied, the answer is positive.  So therefore, the answer is 8.

So remember that the type of exponent is an indicator as to what type of integer you’ll get for an answer.

Try these examples for yourself.  -4and  -33