7-1 integer exponents - geary county usd 475

Holt Algebra 1

7-1 Integer Exponents

Bellringer Evaluate each expression for the given values of the variables.

1. x3y2 for x = –1 and y = 10

2. for x = 4 and y = (–7)

Write each number as a power of the given base.

3. 64; base 4

4. –27; base (–3)

-100

48/49

43 = 64

(-3)3 = 27

Holt Algebra 1


Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

Objectives

Evaluate and multiply by powers of 10.

Convert between standard notation and scientific notation.

Know:

Do:

Write in Scientific notation 0.00000123

2.1.2 generates and explains a pattern.

Holt Algebra 1


You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 3 3 = 9.

But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.

3125 625 125 25 5

5

Power

Value

55 54 53 52 51 5–1 50 5–2

5 5 5

Holt Algebra 1


When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

Holt Algebra 1


Base

x

Exponent

Remember!

4

Holt Algebra 1


In Your Notes

Holt Algebra 1


Notice the phrase “nonzero number” in the

previous table. This is because 00 and 0 raised to

a negative power are both undefined. For

example, if you use the pattern given above the

table with a base of 0 instead of 5, you would

get 0º = . Also 0–6 would be = . Since

division by 0 is undefined, neither value exists.

Holt Algebra 1


2–4 is read ―2 to the negative fourth power.‖

Reading Math

Holt Algebra 1


Check It Out! Example 1

A sand fly may have a wingspan up to 5–3 m. Simplify this expression.

5-3 m is equal to

Holt Algebra 1


In (–3)–4, the base is negative because the

negative sign is inside the parentheses. In –3–4

the base (3) is positive.

Caution

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Check It Out! Example 2 Simplify.

a. 10–4

b. (–2)–4

c. (–2)–5

d. –2–5

In Your Notes

Holt Algebra 1


Check It Out! Example 3a

Evaluate the expression for the given value of the variable.

p–3 for p = 4

Substitute 4 for p.

Evaluate exponent.

Write the power in the

denominator as a product.

Evaluate the powers in

the product.

In Your Notes

Holt Algebra 1


Check It Out! Example 3b

Evaluate the expression for the given values of the variables.

for a = –2 and b = 6

2

Substitute –2 for a and 6 for b.

Evaluate expressions with

exponents.

Write the power in the

denominator as a product.

Evaluate the powers in

the product. Simplify.

In Your Notes

Holt Algebra 1


What if you have an expression with a negative

exponent in a denominator, such as ?

or Definition of a negative exponent.

Substitute –8 for n.

Simplify the exponent on the right side.

So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.

An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.

Holt Algebra 1



Simplify.

a. 2r0m–3

b. c.

rº = 1 and .

In Your Notes

Holt Algebra 1


Holt Algebra 1


//localhost/Users/mrfrench/Documents/Professional Files/Junction City Files/Junction City High School/Algebra 1/Holt Alg 1/Smartboard Lessons/Semester 2/Chapter 7/7-1 & 7-2/7-2 Exploritory.notebook

Holt Algebra 1


The table shows relationships between several powers of 10.

Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left.

Holt Algebra 1


The table shows relationships between several powers of 10.

Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right.

Holt Algebra 1


In Your Notes

Holt Algebra 1


You may need to add zeros to the right or left of a number in order to move the decimal point in that direction.

Writing Math

Holt Algebra 1



Find the value of each power of 10.

a. 10–2 c. 1010 b. 105

10,000,000,000 100,000 0.01

Start with 1 and move the decimal point two places to the left.

Start with 1 and move the decimal point five places to the right.

Start with 1 and move the decimal point ten places to the right.

In Your Notes

Holt Algebra 1


If you do not see a decimal point in a number, it is understood to be at the end of the number.

Reading Math

Holt Algebra 1



Write each number as a power of 10.

a. 100,000,000 b. 0.0001 c. 0.1

The decimal point is eight places to the right of 1, so the exponent is 8.

The decimal point is four places to the left of 1, so the exponent is –4.

The decimal point is one place to the left of 1, so the exponent is –1.

In Your Notes

Holt Algebra 1


You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1.

Multiplying by Powers of 10

Holt Algebra 1



Find the value of each expression.

a. 853.4 105

853.4 0 0 0 0 Move the decimal point 5

places to the right. 85,340,000

b. 0.163 10–2

0.0 0163

0.00163

Move the decimal point 2

places to the left.

In Your Notes

Holt Algebra 1


Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied.

The first part is a number that is greater than or equal to 1 and less than 10.

The second part is a power of 10.

In Your Notes

Holt Algebra 1


Standard form refers to the usual way that numbers are written—not in scientific notation.

Reading Math

Holt Algebra 1


Check It Out! Example 4a

Use the information above to write Jupiter’s diameter in scientific notation.

143,000 km

1 4 3 0 0 0

5 places

Count the number of places

you need to move the

decimal point to get a

number between 1 and 10.

Use that number as the exponent of 10.

1.43 105 km

In Your Notes

Holt Algebra 1


Check It Out! Example 4b

Use the information above to write Jupiter’s orbital speed in standard form.

1 3 0 0 0 Move the decimal point 4 places to

the right. 13,000 m/s

In Your Notes

Holt Algebra 1


Order the list of numbers from least to greatest.


Step 1 List the numbers in order by powers of 10.

Step 2 Order the numbers that have the same power of 10

2 10-12, 4 10-3, 5.2 10-3, 3 1014, 4.5 1014, 4.5 1030

In Your Notes

Holt Algebra 1


Holt Algebra 1


Daily Asn

7.1 & 7.2 Practice B Worksheets