Holt Algebra 1

7-4 Division Properties of Exponents

Warm UpSimplify.

1. (x2)3

3. 5.

2.

4.6.

7.Write in Scientific Notation.

8.

Holt Algebra 1

7-4 Division Properties of Exponents

Students will be able to: Use division properties of exponents to evaluate and simplify expressions.

Learning Targets

Holt Algebra 1

7-4 Division Properties of Exponents

52

3

3 3 3 3 3 3 3 3 33 3 3 3

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

55 3 2

3

3 3 33

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify.

A. B.

7 2 52 2 32 4 3 1 xx x

Holt Algebra 1

7-4 Division Properties of Exponents

C.

Simplify.

D.

2512

Holt Algebra 1

7-4 Division Properties of Exponents

Both and 729 are considered to be simplified.

Helpful Hint

Holt Algebra 1

7-4 Division Properties of Exponents

You can “split up” a quotient of products into a product of quotients:

Example:

Writing Math

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify and write the answer in scientific notation

10

35 10

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify and write the answer in scientific notation.

6

8

3.3 103 18

Holt Algebra 1

7-4 Division Properties of ExponentsThe Colorado Department of Education spent about dollars in fiscal year 2004-05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.

The average spending per student is $5,800.

Holt Algebra 1

7-4 Division Properties of ExponentsA 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.

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify.

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify.

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify.

Holt Algebra 1

7-4 Division Properties of Exponents

Therefore,

Remember that What if x is a fraction?.

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify.

343

Holt Algebra 1

7-4 Division Properties of Exponents

Simplify.

23

22yx

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify. 2 3 3

3 3

3 2 9 82 6 4 6

n nm m

3

33

2961nm

3

3

224nm

3

312nm

Holt Algebra 1

7-4 Division Properties of ExponentsSimplify. 42 3

2b ca

HW pp. 471-473/17-45,47-57,62-71