Radical Mathematics

Rational Exponents vs Radical Form.

3 2x32

x

2 4x24

x4 20x4

20

x

Rational Exponents vs Radical Form.

4921

49

3 2731

27204 )( x4

20

x

3 2x32

x ROOTROOT

Power

Power

23 x32

x ROOTROOT

Power

Power

34

8

Note how many different ways rational exponents can be written! AND they all mean

the same thing!!!!!!

4

31

8

31

48

32

27

Note how many different ways rational exponents can be written! AND they all mean

the same thing!!!!!!

2

31

27

31

227

Find the Indicated real nth root (n) of a.

n = 3, a = -27

31

27 3 27- or

Using your calculator……

5 815 :INDF5 2nd Ʌ 815 =

3.82

Using your calculator……

5 815 :INDF52nd yx815 =

3.82

Without using your calculator……

23

25 :INDF

ROOT it! THEN POWER it!

Without using your calculator……

43

16 :INDF

ROOT it! THEN POWER it!

Without using your calculator……

32

27- :INDF

ROOT it! THEN POWER it!

Without using your calculator……

23

25 :IND

FROOT it! POWER it! Then FLIP it!

. 125

1 is 125 125. is 5 5. is 25 ofroot Square 1-3

Without using your calculator……

43

16 :IND

FROOT it! POWER it! Then FLIP it!

. 81 is 8 8. is 2 2. is 16 ofroot Fourth 1-3

Without using your calculator……

32

27- :INDF

ROOT it! THEN POWER it!

Radicals Upgraded!

YOU know……………

44 52 47When we multiply LIKE bases

we ADD exponents.

452 410

When we raise a base to a power we MULTIPLY exponents.

YOU know……………

6

5

x3x

x3

When we divide bases we subtract exponents of like bases.

SO…..What if…………..

44 75

32

When we multiply LIKE

bases we ADD exponents.

So we just add the fractions!

4 75

32

4 2129

Yeah,

there’s more…

457

32

When we raise bases

to a power we multiply exponents.

So we just multiply the fractions!

4 1514

Yeah,

there’s more…

4

4

51

32

When we divide LIKE bases we

Subtract exponents.

4 57

Yeah,

there’s more…

51

32

4

77 75

41

7 75

41

7 2827

773

753

2

41

13

75

32

41

7 7

715

122

7 7 7 715

122

7 84194

31

54

Yeah,

there’s more…

31

31

5

4