Essay Available:

You are here: Home → Math Problem → Mathematics & Economics

Pages:

2 pages/≈550 words

Sources:

No Sources

Level:

APA

Subject:

Mathematics & Economics

Type:

Math Problem

Language:

English (U.S.)

Document:

MS Word

Date:

Total cost:

$ 8.64

Topic:

# Math Problem: Laws of Exponents (Math Problem Sample)

Instructions:

What are three laws of exponents (for multiplication, division, and powers)? Write and explain each law. Why do we use exponents in scientific notation (you can provide an example)?

Write 2 problems containing exponents for your peers to simplify. Return to the discussion to check your peers’ understanding and offer help as needed. Be sure to post the answers at the close of the module.

Content:

Laws of Exponents

Name:

Institution:

Tutor:

Task:

Date:

Laws of Exponents

Repeated multiplication of the same number by itself can be very long and elaborate but the scenario can be simplified in from of shorthand. The shorthand is referred to as an exponent or a power and a perfect example is when a number like 3 is multiplied by itself four times i.e. 3x3x3x3=34. The superscript 4 is referred to as an exponent or power whereas 3 is referred to as the base. The product in this example is pronounced as "three raised to the fourth powerâ€.

The Three Laws of Exponents

Multiplication Law

Ya Yb= Ya+b

When multiplying the same number by itself, the exponents are normally added. This means that powers of the same base are added when being multiplied. An example of this is:

Y4 Y3= Y 7. In this case the base is the same i.e. Y and therefore its exponents are added to get Y7.

The Division Law

Ya /Yb = Y a-b

Exponents of the same base are subtracted from each other in case of division. In this case the base is Y and the exponents are a and b. An example of this is:

Y7 / Y4 = Y 3

The Law of Powers

1 (XY) a = X a Ya

In instances where there are two different factors under the same power, each factor is raised to the same power. In this case the two factors are X and Y under the same power a. An example of this is:

(XY) 5 = X 5 Y5

2 (Ya)b = Y ab

Exponents are multiplied in instances of a power of a power. In this case b is a power of power a and therefore the exponents will be multiplied. An example of this is:

(Y2)3 =Y6

3 Y 1/a = a â€šY

The exponent root of the base is determined in case the exponent is a denominator of 1. In this case the exponent is a and the base is Y. An example of this is

Y 1/5 = 5 â€šY. This means that the fifth root of Y should be determined.

4 Y-a = 1/Ya

In case of a negative power, the base is raised to the equivalent positive power as a denominator of 1. An example of this is:

Y-2 = 1/Y 2

5 Y0 = ...

Get the Whole Paper!

Not exactly what you need?

Do you need a custom essay? Order right now:

### Other Topics:

- What is the Use of RSA Algorithm Research AssignmentDescription: Computers and internet has called for tight privacy protection as users have their sensitive information stored on networks and on computers...12 pages/≈3300 words| 11 Sources | APA | Mathematics & Economics | Math Problem |
- Economics Math Problem Assignment: Maximizing RevenueDescription: a price increase of two dollars will lead to a single less sale. As such, John Deere should ensure that the price of the tractors does not exceed 1900. ...1 page/≈275 words| No Sources | APA | Mathematics & Economics | Math Problem |
- Math Problem (Precalc group 5)Description: Solve each system by substitution. 3x + 4y = 4 x - y = 13. Use the given row transformation to change each matrix as indicated...2 pages/≈550 words| No Sources | APA | Mathematics & Economics | Math Problem |