Exponents 5 2 Vocabulary exponent the number of

Exponents 5 2 =?

Vocabulary exponent – the number of times a number is multiplied by itself. base – the number that is being multiplied. 3 base 8 exponent This is read “ 8 to the 3 rd power” or “ 8 cubed. ” It means 8 x 8.

Evaluating Exponents 5 2 = 2 x 2 x 2 = 32 3 6 = 6 x 6 = 216 4 1. 3 = 1. 3 x 1. 3 = 2. 8561

Exponents with a base of 10 • Any multiple of ten can be expressed as an exponent with a base of ten. • The base is 10. The number of zeroes gives us the exponent. 2 • Example: 100 = 10 4 • 10, 000 = 10 6 1, 000 = 10

Writing in Expanded Form Using Powers of 10 • First, write the problem in expanded form. • Then, change each term to a multiplication of the value and its place. • Change the place values to exponents with powers of 10.

Example 7, 946 7, 000 + 900 + 40 + 6 (7 x 1, 000) + (9 x 100) + (4 x 10) + (6 x 1) 3 2 1 7 x 10 + 9 x 10 + 4 x 10 + 6

Simplify. 1. 2 2 2 8 2. 3 3 81 3. 5 5 5 4. 4 4 4 125 64 5. 6 6 6 7, 776

Powers and Exponents A simple way to think of exponents and powers is as repeated multiplication m • m = m 3

Key Terms o factor: when two or more numbers are multiplied together, each number is called a factor o exponent: an exponent tells how many times a number (called a base) is used as a factor o power: a number that is expressed using a base and an exponent base

Powers and Exponents

Evaluating Powers Find each value. A. 44 44 = 4 4 = 256 B. 73 73 = 7 7 7 Use 4 as a factor 4 times. Use 7 as a factor 3 times. = 343 C. 191 = 19 Use 19 as a factor 1 time.

Evaluating exponents 43 Use 4 as a factor 3 times 4 4 4 = 16 72 Use 7 as a factor 2 times 7 7 = 49 27 Use 2 as a factor 7 times 2 2 = 128 35 Use 3 as a factor 5 times 3 3 3 = 243 106 Use 10 as a factor 6 times 10 10 10 = 1, 000 171 Use 17 as a factor 1 time 171 = 17

Exponents To express a whole number as a power, write the number as the product of equal factors. Then write the product using the base and an exponent. For example, 10, 000 = 10 10 = 104.

Expressing Whole Numbers as Powers Write each number using an exponent and the given base. A. 625, base 5 625 = 5 5 5 is used as a factor 4 times. = 54 B. 64, base 2 64 = 2 2 2 = 26 2 is used as a factor 6 times.

Write each number using an exponent and the given base 343, base 7 7 7 7 = 73 256, base 2 2 2 2 2 = 28 1, 000, 000 base 10 10 10 = 109

Application On Monday, Erik tells 3 people a secret. The next day each of them tells 3 more people. If this pattern continues, how many people besides Erik will know the secret on Friday? On Monday, 3 people know the secret. On Tuesday, 3 times as many people know as those who knew on Monday. On Wednesday, 3 times as many people know as those who knew on Tuesday. On Thursday, 3 times as many people know as those who knew on Wednesday.

Application: Continued On Friday, 3 times as many people know as those who knew on Thursday. Each day the number of people is 3 times greater. 3 3 3 = 35 = 243 On Friday 243 people besides Erik will know the secret.

Scientists and mathematicians use exponential notation To describe very large and very small numbers. The average distance between the earth and the sun is 1 AU (astronomical unit) or about 93 million miles. We can write that number as • Ninety three million • 93, 000 • 93 x 106 What advantage is there in using exponential notation to write very large numbers?