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# Laws of Exponents - PowerPoint PPT Presentation

Laws of Exponents. Objective: TSW simplify powers. TSW simplify radicals. TSW develop a vocabulary associated with exponents. TSW use the laws of exponents to simplify. Exponents. The lower number is called the base and the upper number is called the exponent.

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## PowerPoint Slideshow about ' Laws of Exponents' - bevis-browning

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### Laws of Exponents

Objective:

TSW simplify powers.

TSW develop a vocabulary associated with exponents.

TSW use the laws of exponents to simplify.

• The lower number is called the base and the upper number is called the exponent.

• The exponent tells how many times to multiply the base.

exponent

7

3

base

power

7

• To square a number, just multiply it by itself.

3 squared =

= 3 x 3 = 9

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

13² = 169

Perfect Squares

• A square root goes the other direction.

• 3 squared is 9, so the square root of 9 is 3

9

3

- The inverse operation of raising a number to a power.

• For Example, if we use 2 as a factor with a power of 4, then we get 16. We can reverse this by finding the fourth root of 16 which is 2.

= 2

4

16

• In this problem, the 16 is called the radicand, the 4 is the index, and the 2 is the root.

• The symbol is known as the radical sign. If the index is not written, then it is understood to be 2.

• The entire expression is known as a radical expression or just a radical.

• Simplify:

a) c)

b) d)

3

4

27

81

3

8

16

• Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them.

• Those operations are called the “Laws of Exponents.”

• A nonzero based raise to a zero exponent is equal to one

0

= 1

a

)

(

1

-n

a

______

=

n

a

A nonzero base raised to a negative exponent is the reciprocal of the base raised to the positive exponent.

1.

2.

3.

4.

### Scientific Notation

Objective:

TSW rewrite numbers in scientific notation

TSW perform operations with numbers in scientific notation.

TSW solve real-world problems using numbers in scientific notation.

• When we write a number greater than or equal to ten in scientific notation, we use three steps:

• 1. place the decimal point just right of the first nonzero digit

• 2. count the number of places the decimal point moved to the left

• 3. multiply the number in step one by 10ª (a is the number of places the decimal point moved) to indicate where the decimal point should be.

Example scientific notation, we use three steps:

• Write 7,024,000 in scientific notation

Example scientific notation, we use three steps:

• Write 476.23 in scientific notation.

• When we write a number between zero and one in scientific notation, we use three steps:

• 1. place the decimal point just to the right of the first nonzero digit

• 2. count the number of places the decimal point moved to the right

• 3. multiply the number in step one by 10ˉª (a is the number of places the decimal point moved) to indicate where the decimal point should be

Example notation, we use three steps:

Write 0.0652 in scientific notation.

Example notation, we use three steps:

1. Write these numbers in standard notation:

a.) 4.6 x 10ˉ³

b.) 4.6 x 10

2. Saturn is about 875,000,000 miles from the sun. What is this distance in scientific notation?

6

Answers notation, we use three steps:

1. a.) 0.0046

b.) 4600000

2. 8.75 x 10

8

Computing with Scientific Notation notation, we use three steps:

• You can multiply and divide numbers written in scientific notation. (Use the Laws of Exponents!)

• To multiply powers with the same bases, add the exponents

• To divide powers with the same base, subtract the exponents

(3.2 x 10 notation, we use three steps: ²) x (2 x 10³)

• Step 1: Multiply the first pair of factors from each

(3.2 x 2) = 6.4

• Step 2: Multiply the second pair of factors ( the ones written in exponential form)

10² x 10³ = 10 = 10

• Step 3: Combine the products

6.4 x 10

2 + 3

5

5

Examples notation, we use three steps:

5

• 1. (5.4 x 10 ) x (4.6 x 10³)

• 2. (8.4 x 10³) x (2.1 x 10 )

• 3. (1.2 x 10 ) x (9.6 x 10²)

-4

-4

Answers notation, we use three steps:

9

• 1. 2.484 x 10

• 2. 4 x 10

• 3. 1.25 x 10

7

-7

Adding and Subtracting notation, we use three steps:

• You can also add and subtract with numbers written in scientific notation as long as the second factors are the same.

Example notation, we use three steps:

8

• About 8.73 x 10 people in the world speak Mandarin Chinese. About 3.22 x 10 people speak Spanish. In scientific notation, how many more people speak Mandarin Chinese than Spanish?

8

Answer notation, we use three steps:

8

8

• (8.73 x 10 ) – (3.22 x 10 )

• (8.73 – 3.22) x 10

• 5.51 x 10 more people speak Mandarin Chinese than Spanish

8

8

Example notation, we use three steps:

7

• The Atlantic Ocean has an area of 3.342 x 10 square miles. The Artic Ocean has an area of 5.105 x 10 square miles. In scientific notation, what is the combined area of the two oceans?

6