Warm UpSimplify.

1.

3.

5.

2.

4.

6.

(10²)³

ObjectiveUse division properties of exponents

to evaluate and simplify expressions.

A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors.

Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2.

Simplify.

Finding Quotients of Powers

A. B.

C.

Simplify.

Finding Quotients of Powers

D.

Both and 729 are considered to be simplified.

Helpful Hint

Try This!

a.

Simplify.

b.

Try this!

Simplify.

c. d.

A power of a quotient can be found by first writing the numerator and denominator as powers.

Notice that the exponents in the final answer are the same as the exponent in the original expression.

Simplify.

Finding Positive Powers of Quotient

Use the Power of a Quotient Property.

Simplify.

Simplify.

Finding Positive Powers of Quotient

Use the Power of a Product Property.

Use the Power of a Product Property:

Simplify and use the Power of a Power Property:

Simplify.

Finding Positive Powers of Quotient

• Use the Power of a Product Property.

• Use the Power of a Product Property:

• Use the Power of a Product Property:

• Use the Power of a Product Property:

Try This!

Simplify.

Use the Power of a Quotient Property.

Simplify.

Try this!Simplify.

Try This!Simplify.

Simplify.

Finding Negative Powers of Quotients

Rewrite with a positive exponent.

and

Use the Powers of a Quotient Property .

Simplify.

Finding Negative Powers of Quotients

Simplify.

Finding Negative Powers of Quotients

Rewrite each fraction with a positive exponent.

Use the Power of a Quotient Property.

Use the Power of a Product Property:

(3)2 (2n)3 = 32 23n3and (2)2 (6m)3 = 22

63m3

1

241

21

12

Divide out common factors.

Simplify.

Finding Negative Powers of Quotients

Simplify.

Square and cube terms.

Whenever all of the factors in the numerator or the denominator divide out, replace them with 1.

Helpful Hint

Try This!

Simplify.

93=729 and 43 = 64.

Use the power of a Quotient Property.

Rewrite with a positive exponent.

Try This!

Simplify.

Rewrite with a positive exponent.

Use the Power of a Power Property: (b2c3)4= b2•4c3•4 = b8c12 and (2a)4= 24a4= 16a4.

Use the Power of a Quotient Property.

Try This!Simplify.

Rewrite each fraction with a positive exponent.

Use the Power of a Quotient Property.

Use the Power of a Product Property: (3)2= 9.

Add exponents and divide out common terms.