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EVALUATING EXPONENTS

Learn the rules for determining the sign of exponents with negative bases. Even powers result in positive answers, while odd powers yield negative results. Practice problems included.

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EVALUATING EXPONENTS

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  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. 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

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