1. EVALUATING EXPONENTS

2. Let’s review the odd/even rule with and without ( ):
EVEN POWERS:
In this first one, BOTH the
negative sign and the 2 are to the
4th power so there are 4 negatives (even number so positive).
In the second one, ONLY the 2 is to the
4th power because there are no ( )…I call the negative sign a ZAPPER!
AFTER you simplify the power, then think of the negative sign as multiplying by -1. In order of operations, you do the power first and multiply by -1 AFTER you simplify the power.

3. Let’s review the odd/even rule with and without ( ):
ODD POWERS:
In the first one, BOTH the
negative sign and the 2 are to the
3rd power…so there are 3 negatives, which is an odd number. The answer is NEGATIVE.
In the second one, ONLY the 2 is to the
3rd power…the negative sign is a ZAPPER.
AFTER you simplify the power, you multiply by -1. There is only 1 negative in this problem and 1 is an odd number so the answer is NEGATIVE.
So for different reasons,
negative bases raised to
an ODD power are ALWAYS
NEGATIVE!

4. So now you try these:
6 negatives is POSITIVE
1 negative is NEGATIVE

5. There is ONLY 1 NEGATIVE! WHY?
When there are no ( ), only the base
is raised to the power and the negative sign
is the same as multiplying by a -1 AFTER the power
is simplified…therefore the answer is NEGATIVE
There are 5 negatives. Why?
When the negative is inside the ( ), it’s raised to the power of 5.
An odd number of negatives is NEGATIVE

6. TRY THIS: How many negatives are there in this problem?
7 (which is odd).
There are 6 negatives from the power and another negative (a zapper)
outside the ( )
How many negatives are there in this problem?
6 (which is even).
There are 5 negatives from the power and another negative (a zapper)
outside the ( )

7. Try this: YOU CANNOT DISTRIBUTE THE 16 BECAUSE
ORDER OF OPERATIONS SAYS THAT YOU MUST SIMPLIFY
INSIDE THE ( ), THEN DO THE EXPONENT FIRST!!!

8. Do what’s in the ( ) first:
Now simplify the exponents:
Simplify the numerator:
Once the numerator and denominator are simplified, simplify the fraction:

9. TRY THIS: DO NOT DISTRIBUTE THE FIRST NEGATIVE SIGN UNTIL
AFTER YOU SIMPLIFY
WHAT’S INSIDE THE PARENTHESES
AND
AFTER YOU SIMPLIFY THE OUTSIDE EXPONENT.

10. Do the exponent inside the ( ) and ++ for the 25:
Keep simplifying in the ( ):
Keep simplifying in the ( ):
Now do the power:
Add:

11. You always plug in negative
TRY THIS:
REMEMBER:
You always plug in negative
numbers with ( )

12. You always plug in negative
numbers with ( )!
You can go + + on the 3 because the power is on the OUTSIDE.
Simplify the ( )
Simplify the exponents
Multiply

13. TRY THIS:
Only the y is raised to the 2nd power

14. Plug in negative bases in ( )
You can do ++ on the 3 because it’s not raised to a power
The -4 is squared so it is +16 because it’s an even power
Multiply

15. TRY THIS:
Make sure you always simplify the EXPONENT 1st, then apply the negative
sign given in the problem…In other words, YOU CAN’T GO + + BEFORE
YOU DO THE EXPONENT INSIDE THE ( )!!!

16. Plug in the negative base in ( ):
Simplify the exponents:
Simplify the negative signs and add:

17. TRY THIS:

18. Plug in the negative base in ( )
Numerator: Simplify inside the ( )
Denominator: Simplify the exponents
Numerator: Simplify inside the ( )
Denominator: Add
Numerator: Simplify the exponents
Finally: Simplify the fraction