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Objectives The student will be able to: 1. divide monomials. 2. simplify negative exponents. SOL: A.2ab Designed by Skip Tyler, Varina High School

Objectives The student will be able to: 1. divide monomials. 2. simplify negative exponents. SOL: A.2ab Designed by Skip Tyler, Varina High School

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ObjectivesThe student will be able to:

1. divide monomials.

2. simplify negative exponents.

SOL: A.2ab

Designed by Skip Tyler, Varina High School

When dividing monomials, subtract the exponents.

1.

2.

Dividing Monomials

= m6 n3

5

2

b

b

7 5

2

m n

mn

= b5-2b b b b b

b b

= b3

= m7-1n5-2

= xy

3. x3y7

x2 y6

4. 81a8b3

9a5b

= 9a3b2

8 38-5 3-1

5

81a b9a b

9a b

672362

73 yx

yx

yx

Simplify 2 7

5

64g h

16gh

1. 48g2h2

2. 48gh2

3. 4g2h2

4. 4gh2

5. 3m3n3

3m3n2 = 1m0n

Here’s a tricky one!

What happened to the m?

= n

3 3

3 2

3m n 3m m m n n n

3m n 3m m m n n

They canceled out!

There are no m’s left over!This leads us to our next rule…

3

31

m

m

Zero ExponentsAnything to the 0 power is equal to 1.

a0 = 1True or False?

Anything divided by itself equals one.True!

See for yourself!

3

3

3 x m1 1 1

3 x m

0 0 03 1 x 1 m 1

A negative exponent means you move the base to the other side of the fraction and make the exponent positive.

-n n-n n

n -n

a 1 1 aa or = a

1 a a 1

Negative Exponents

Notice that the base with the negative exponent moved and became positive!

Simplify.

-4 04

1x and y 1

x

6. x-4 y0

You can not have negative or zero exponents in your answer.

4 4

1 1

x

1

x

1. p2

2. p12

3. .

4. .

Simplify -7

-5

p

p

12

1

p

2

1

p

Simplify.

7. 3r4s2

18r3s44 3 2 41

r s6

21rs

6

2

r

6s

You can’t leave the negative exponent!

There is another way of doing this without negative exponents.

If you don’t want to see it, skip the next slide!!!

Simplify (alternate version).

7. 3r4s2

18r3s4

Look and see (visualize) where you have the larger exponent and leave the variable in that location. Subtract the smaller exponent from the larger one.

In this problem, r is larger in the numerator and s is larger in the denominator.

4 2 4-3

3 4 4-2

3r s 1r

18r s 6s 2

r

6s

Notice that you did not have to work with negative exponents! This method is quicker!

Simplify.

8. x 3

x4

7

1

x

Get rid of the negative exponent.

3

4 3 4

x 1

x x x

9. r 5s 2

r3s 3

8

s

r

Get rid of the negative exponents.

Simplify.

5 2 3

3 3 5 3 2

r s s

r s r r s

10. x 3y2 2

4x2 3

x 6y4

43 x6

4

12

y

64x

Get rid of the parentheses.

Simplify.

23 2

32

x y

4x

Get rid of the

negative exponents.

4

3 6 6

y

4 x x

x 6y4

43 x6

1. .

2. .

3. .

4. .

Simplify

22 1

33

-3x

2x

y

y

11

9x

8y

11

-9x

8y

7

-9x

8y

7

9x

8y