Exponents and Scientific Notation

P.2

Definition of a Natural Number Exponent If b is a real number and n is a natural

number,bn bbb... b

bn is read “the nth power of b” or “ b to the nth power.” Thus, the nth power of b is defined as the product of n factors of b. Furthermore, b1 = b

The Negative Exponent Rule

If b is any real number other than 0 and n is a natural number, then

b n 1

bn

23

9

1

3

12 Senteo Question

To set the properties right click and selectSenteo Question Object->Properties...

The Zero Exponent Rule

If b is any real number other than 0,b0 = 1.

The Product Rule

b m · b n = b m+n

When multiplying exponential expressions with the same base, add the exponents. Use this sum as the exponent of the common base.

yxyx 41143 1283 yx

The Power Rule (Powers to Powers)

(bm)n = bm•n

When an exponential expression is raised to a power, multiply the exponents. Place the product of the exponents on the base and remove the parentheses.

334x 964x

The Quotient Rule

When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator. Use this difference as the exponent of the common base.

bm

bnbm n

Example

Find the quotient of 43/42

4444

4 1232

3

Solution:

Senteo QuestionTo set the properties right click and selectSenteo Question Object->Properties...

Products to Powers

(ab)n = anbn

When a product is raised to a power, raise each factor to the power.

Simplify: (-2y)4.

(-2y)4 = (-2)4y4 = 16y4

Text Example

Solution

A. -16y4

B. -8y4

C. 16y4

D. 8y4

Senteo QuestionTo set the properties right click and selectSenteo Question Object->Properties...

Quotients to Powers

When a quotient is raised to a power, raise the numerator to that power and divide by the denominator to that power.

n

nn

b

a

b

a

Example

Simplify by raising the quotient (2/3)4

to the given power.

81

16

3

2

3

24

44

Solution:

Senteo QuestionTo set the properties right click and selectSenteo Question Object->Properties...

The number 5.5 x 1012 is written in a form called scientific notation. A number in scientific notation is expressed as a number greater than or equal to 1 and less than 10 multiplied by some power of 10. It is customary to use the multiplication symbol, x, rather than a dot in scientific notation.

Scientific Notation

Text Example

Write the following number in decimal notation: 2.6 X 107

a. 2.6 x 107 can be expressed in decimal notation by moving the decimal point in 2.6 seven places to the right. We need to add six zeros.2.6 x 107 = 26,000,000.

Solution:

Senteo QuestionTo set the properties right click and selectSenteo Question Object->Properties...

Write the following number in decimal notation

1.016 X 10-8

b. 1.016 x 10-8 can be expressed in decimal notation by moving the decimal point in 1.016 eight places to the left. We need to add seven zeros to the right of the decimal point.

1.016 x 10-8 = 0.00000001016.Senteo QuestionTo set the properties right click and selectSenteo Question Object->Properties...

Write each number in scientific notation. a. 4,600,000 b. 0.00023

Solution

a. 4,600,000 = 4.6 x 10? 4.6 x 106Decimal point moves 6 places

b. 0.00023 = 2.3 x 10? 2.3 x 10-4Decimal point moves 4 places

Text Example