The document discusses scientific notation and operations with exponents: 1) Addition and subtraction require that bases and exponents match, then coefficients are added or subtracted. 2) Multiplication is done by adding the exponents of the same bases. 3) Division is done by subtracting the exponents of the same bases.

2. +Addition – like terms
-all variables and exponents must match.
– add coefficients
3 2 3 2 3 2
4x y 7x y 11 x y

3. • Product of Powers(Multiplication)
– add exponents of the same bases.
3 2 3 2 6 4
4x y 7x y 28 x y

4. Power of a Product –distribute the
power throughout the product.
3 3 3
xy x y

5.  Power to a Power – multiply all exponents
of the bases effected by the exponent.
3 2 3 3 3 3 3
2 9 6
4x y 4x y 64x y

6. Quotient of Powers (Division)
– subtract exponents of the same bases.
3 2 2
4x y x
5 3
12 xy 3y

7. Power of a quotient – distribute the
power to the numerator and denominator.
2 2
4x 16 x
2
y y

8. • Zero exponents
-Anything to the zero power equals
one!!!!!!!!!!!!!!!!!
a7 a7
7
a7 7
a0 but 7
1 a0 1
a a

9. • Negative exponents – move any base with
negative exponents to its reciprocal and
make the exponent positive.
a5 5 7 2 a5 aaaaa 1
a a but 7
a7 a aaaaaaa a2
-2 1
a
a2

10. index radical
Base
2 AKA
3 radicand

11. Index 1
Index
2 2
3 3
base

12. 3
2 3 2
3 3

13. 85,000,000 * 1200
7 3
8.5 *10 1.2 *10
7 3
(8.5 *1.2) 10 *10
10
10.2 *10
1 10
1.02 *10 *10
11
1.02 *10

14. • Addition and Subtraction – bases and
exponents must be the same – add or
subtract coefficients.
• Multiply – add the exponents
• Divide - subtract the exponents
• Zero exponents – equals one
• Negative exponents – move that base to
the reciprocal position!!

15. • Pg 333: 3-17 and 24-35