Day 1 : Laws of Exponents

ReviewBook sections 7.1 and 7.4

a0 = 1 b-1 = (am)(an) = am + n

= am – n (ab)m = ambm

Do not copy:

Roots and Rational Exponents

If

Then

New Law: Rational Exponents

= 3

Roots and Rational Exponents

If

Then

New Law: Rational Exponents

You may choose whether to find the root

or the power first!

You may choose whether to find the root

or the power first!

Simplify Exponents with Fractions

1.

2.

3.

You try on your marker board

The teacher will show you 10 problems on the smart board. The student will rearrange the form of the equation from:

Exponential to Radical

or

Radical to Exponential

2

1

x

Convert from Exponential to Radical (marker board)

5

2

a

3

1

1

c

3

2

9

2

3

3

x

25 a

31

c 3 c

23 9 3 81

3 327 3 33

33 27

39

33

Everyone to marker board and work with your number partner

c

Convert from Radical to Exponential (marker board)Don’t simplify anything!

3 m

23 4

3 24

23 8

2

1

c

3

1

m

3

2

4

3

2

4

3

2

8

Back to Notes: Simplify ExponentialsAssume all variables are positive

4. 5.

6. 7.

2

7

f

ff 3

3

2

642

3 6424 16

23

3

2

k

k

9

8 2

3

k

k k9

8

103 98 ff

1372 f

2

13f

Simplify Radicals8. 9.

10. 11. 12.

3 125

106425 zyx

5

4

5

5

5

54

3 555

5

5325 zyx 25x

5x

3 756332 rqpm

3 26363 48 rqrqpm

3 222 42 rqqrmp

Practice Laws of Exponents

13. 14.

262

1296

16

8

cba

cba

2

1034 cba

)9(

44

60

m

hg

6

4

9

4

h

m

More Simplifying with exponentsAssume all variables are positive

15. 16.

17. 18.

323

5 32

8

21

x 2

1

1

x

x

1

x

x

x

x

64

3

16

1y

6

4 316

1y

8

6y

5

2

1

32

1

30-60-90 Right Triangle

2x

60°

60°

60°

45-45-90 Right Triangle

X

THEN

49142 xx

1. Simplify 2. Find x 3. Find x 4. Simplify 5. Simplify.

)5()3( 32220 bcba

xq

q

q

2

1

3

7

4 816y

Extra Practice on HW 7.1: Work this out in your math notebook.

Assume all variables are positive.

32

64

49142 xx

1. Simplify 2. Find x 3. Find x 4. Simplify 5. Simplify.

)5()3( 32220 bcba

xq

q

q

2

1

3

7

4 816y

Extra Practice on HW 7.1: Work this out in your math notebook.

Assume all variables are positive.

32

64

22y4

745

c

b

6

11x 16

17x

6. Simplify. 7. Simplify. 8. Simplify. 9. If 4 is the leg of a 45-45-90 triangle, find the other sides.

10. Simplify.

Extra Practice on HW 7.1: Work this out in your math notebook.

Assume all variables are positive.

5

3

3

17

v

3 11554 wx 293

2720

10

5

cb

cba

1

2

1

3

6. Simplify. 7. Simplify. 8. Simplify. 9. If 4 is the leg of a 45-45-90 triangle, find the other sides.

10. Simplify.

Extra Practice on HW 7.1: Work this out in your math notebook.

Assume all variables are positive.

5

3

3

17

v

3 11554 wx 293

2720

10

5

cb

cba

424

1

cb

4.3

5 23

5

17

v

not

vv

or

v

3 223 23 xwxw

424 and3

3

1

2

1

3

HOMEWORK 7.1 due next class!!!

33 Questions