For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Properties of Exponents

- You multiply powers with the same base by adding the exponents.
- You divide powers with the same base by subtracting the exponents.
- Multiplying powers is used for performing calculations with very large numbers such as the speed of light.
- Dividing powers is used for performing calculations with very small numbers such as the size of cells.

### Properties of Exponents

5

^{− 4}×5^{3}=- 5
^{ − 4 + 3}= - 5
^{ − 1}=

[1/5]

− 2 ×( − 2)

^{− 3}=- ( − 2)
^{1 − 3}= - ( − 2)
^{ − 2}= - [1/(( − 2)
^{2})] =

[1/4]

2t

^{3}·5t^{9}=- 10t
^{3 + 9}=

10t

^{12}3

^{4}·3^{− 1}=- 3
^{4 − 1}= - 3
^{3}=

274

14x

^{6}÷2x^{4}=- 7x
^{6 − 4}=

7x

^{2}(3 + 2) ÷5

^{4}=- 5 ÷5
^{4}= - 5
^{1}÷5^{4}= - 5
^{1 − 4}= - 5
^{ − 3}= - [1/(5
^{3})] =

[1/125]

[(4

^{4})/(4^{6})] =- 4
^{4 − 6}= - 4
^{ − 2}= - [1/(4
^{2})] =

[1/16]

x

^{5}÷3x^{2}÷2x =- [(x
^{5})/(3x^{2})] ÷2x = - [1/3]x
^{5 − 2}÷2x = - [1/3]x
^{3}÷2x = - [1/6]x
^{3 − 1}=

[1/6]x

^{2}[(7.6 ×5

^{21})/(2 ×5^{19})] =- 3.8 ×5
^{21 − 19}= - 3.8 ×5
^{2}= - 3.8 ×25 =

95

The distance between Earth and Mercury is about 36 × 10

^{6}mi. Light travels at a speed of about 1.1 × 10^{7}mi/min. Estimate to the nearest tenth minute how long light from Mercury takes to travel to Earth. Use the formula time = [distance/speed].- time = [(36 ×10
^{6}mi)/(1.1 ×10^{7}mi/min)] = - 32 ×10
^{6 − 7}min = - 32 ×10
^{ − 1}min = - 32 ×[1/10] min =

3.2 min

The sun's diameter is about 1.4 × 10

^{6}km. Mercury's diameter is about 4.9 × 10^{3}km. How many times greater, to the nearest ones place, is the sun's diameter than Mercury's diameter?- [(1.4 ×10
^{6}km)/(4.9 ×10^{3}km)] = - 0.286 ×10
^{6 − 3}km = - 0.286 ×10
^{3}km =

286 times

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Properties of Exponents

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Multiplying Powers with the Same Base
- Multiplying Expressions with Exponents
- Dividing Powers with the Same Base
- Dividing Expression with Exponents
- Dividing Expression with Exponents
- Extra Example 1: Multiplying Expressions with Exponents
- Extra Example 2: Dividing Expression with Exponents
- Extra Example 3: How Long Sunlight Takes to Reach Saturn
- Extra Example 4: Sun's Diameter and Earth's Diameter

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:26
- Exponent
- Power
- Multiplying Powers with the Same Base 1:04
- Example: Multiplying Powers with the Same Base
- Multiplying Expressions with Exponents 2:25
- Examples
- Dividing Powers with the Same Base 3:24
- Example: Dividing Powers with the Same Base
- Dividing Expression with Exponents 3:59
- Example: How Long Sunlight Takes to Reach the Comet
- Dividing Expression with Exponents 6:44
- Example: How Long Sunlight Takes to Reach Earth
- Extra Example 1: Multiplying Expressions with Exponents 8:22
- Extra Example 2: Dividing Expression with Exponents 8:46
- Extra Example 3: How Long Sunlight Takes to Reach Saturn 9:12
- Extra Example 4: Sun's Diameter and Earth's Diameter 10:34

0 answers

Post by John White on August 9, 2016

if I have 2x^2 + 2x^2 the and is 4 x^2 not not 4x^4

you only add exponents with the same base when multiplying.

0 answers

Post by misrak taye on March 9, 2014

ooooooooooooowhat is the signes mean????????????????????????

0 answers

Post by Saakshi Dhingra on September 22, 2013

shouldnt it be multiplying the two numbers with exponents instead of adding them at 1:04?

1 answer

Last reply by: Professor Fung

Thu Aug 1, 2013 3:51 AM

Post by Ming Jin on July 31, 2013

the formula is WRONG!

1 answer

Last reply by: Professor Fung

Thu Aug 1, 2013 3:43 AM

Post by Jeff Mitchell on January 8, 2011

This lecture is titled "multiplication" but the first example is incorrectly deplicted as

adding numbers with the same base and so the whole discussion is wrong and confusing. It should be displayed a^M * a^N = a^(M+N) but is instead illustrated as a^M + a^N which does not equate to a^(M+N).

~Jeff