Fundamentals of Math

Fundamentals of Mathematics

Powers of 0 or 1

Power of Zero

Power of One

Any base raised to the 0 power is 1, but watch out for negatives.

Any base raised to the 1 power is the base.

24 0 = 1 and −24 0 = −1

4 1 = 4 and −27 1 = −27

Practice 3.1.1

Directions: Simplify the following expressions.

1. (−7) 3

2. −2 4

3. −5 2

4. (−3) 5

5. 508 0

6. −42 0

7. −4 0

8. (−5) 0

9. 3 −1

10. (−2) −1

Answer Key on Page 118

Operations with Exponents

Definition

Example

When multiplying two or more terms together with like bases. Keep the exponents the same and add the exponents. When dividing two or more terms together with like bases. Keep the exponents the same and subtract the exponents. When raising an exponent to an exponent, keep the base the same and multiply the exponents. When a quotient (or fraction) is being raised to an exponent the exponent gets applied to both the numerator and denominator.

8 7 × 8 5 = 8 7+5 = 8 12

×

Multiplying

+

=

9 8 9 2

= 9 8−2 = 9 6

−

Dividing

=

IMPORTANT: If the bases between terms are not the same the aforementioned rules do NOT apply.

×

(5 6 ) 3 = 5 6×3 = 5 18

( ) =

Power Raised to a Power

=

Quotient Raised to a Power

3

2 3 7 3

2 7

( ) =

(

)

=

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