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1.7 Powers and Roots

POWERS AND EXPONENTS

When a number is multiplied by itself several times, instead of writing each repetition of the multiplication, it is easier to use exponential notation. For example, 12 × 12 × 12 × 12 × 12 × 12 would be 12 multiplied to itself 6 times or 126. The number being multiplied is called the base and the number of times it is multiplied by itself is called the exponent. In the above case, the base is 12 and the exponent is 6. When a number has an exponent of 2, it is said to be squared. When the exponent is 3, the number is said to be cubed. When the exponent is 4, the number is expressed as the base to the fourth power, and so on.

Example 1 - Write 6 × 6 × 6 in exponential notation and in words. Solve.

6 × 6 × 6 = "six cubed" or 63. 63 = 216.

SQUARE ROOT


Powers can also be worked backwards to find the square root of the number. The number whose root you want to find will appear under a square root sign: √x. The square root of a number x is the number that would have to be squared in order to get x.

For example, the square root of 4 would be 2, since 22 = 4.

Example 2 - Find √49

√49 = 7 because 7 × 7 = 49
 

Perfect squares are numbers having a square root that is an integer. Not all numbers are perfect squares. In these situations, divide to see whether the number can be separated into two factors: the first factor is a number that is a perfect square while the rest stays as a square root.

Example 3  - Find √18
Divide into √(9x2). The square root of 9 is an integer (3), so it can be taken outside of the square root symbol. The 2 remains under the square root symbol, because it is not a perfect square. √18 = 3 × √ 2.

NWCG Latest Announcements

The Incident Position Standards and Next Generation Position Task Book are now available for Status/Check-In Recorder (SCKN)

Date: August 27, 2024
Contact: Incident Planning Subcommittee 

NWCG is excited to announce that the NWCG Incident Position Standards for Status/Check-In Recorder, PMS 350-32, NWCG Position Task Book for Status/Check-In Recorder (SCKN), PMS 311-32, and Checking In Resources Customer Service Job Aid, J-111 are now available.

The Performance Support Package, which for SCKN includes the Incident Position Standards, Next Generation Position Task Book, and job aid were developed through the Incident Performance and Training Modernization (IPTM) effort. The Performance Support Package will support trainees, those qualified in the position, and evaluators.

References:

NWCG Status/Check-In Recorder Position Page

NWCG Incident Position Standards for Status/Check-In Recorder, PMS 350-32

NWCG Position Task Book for Status/Check-In Recorder (SCKN), PMS 311-32

Checking In Resources Customer Service Job Aid, J-111

The Next Generation Position Task Book and Incident Position Standards are now available for Safety Officer, Field (SOFF)

Date: July 26, 2024
Contact: Risk Management Committee 

NWCG is excited to announce that the NWCG Incident Position Standards for Safety Officer, Field, PMS 350-81 and NWCG Position Task Book for Safety Officer, Field (SOFF), PMS 311-81 are now available.

The Safety Officer, Field (SOFF) is responsible for monitoring operations on an incident from a risk management perspective to provide for the welfare of incident resources and the public. The new Incident Position Standards and Next Generation Position Task Book are developed through the Incident Performance and Training Modernization (IPTM) effort.

References:

NWCG Safety Officer, Field (SOFF) Position

NWCG Incident Position Standards for Safety Officer, Field, PMS 350-81

NWCG Position Task Book for Safety Officer, Field (SOFF), PMS 311-81

Updated NWCG Standards for Electronic Documentation (eDoc), PMS 277

Date: July 25, 2024
Contact: Incident Planning Subcommittee 

The Incident Planning Subcommittee has updated the NWCG Standards for Electronic Documentation (eDoc), PMS 277.

The NWCG Standards for Electronic Documentation (eDoc) establishes the standards for collection and retention of records on wildland fires. This July 2024 update will provide incident management teams the most current standards required to maintain incident records and submit them to host units at the close of an incident.

References:

NWCG Standards for Electronic Documentation (eDoc), PMS 277

eDoc Box Directory (zip file)

NWCG Off-Highway Vehicle Typing Standard Request for Comment

Date: July 24, 2024
Contact: Mobile Fire Equipment Subcommittee 

The Mobile Fire Equipment Subcommittee has released Equipment Bulletin 24-002 NWCG Off-Highway Vehicle (OHV) Typing Standard - Request for Comment. This bulletin outlines the proposed NWCG OHV typing standard, as well as the business need for establishing the standard. Comments on the proposed standard will be accepted through August 15th using the comment form linked below.

References:

ETC-EB-2024-02: NWCG Off-Highway Vehicle (OHV) Typing Standard - Request for Comment

NWCG Off-Highway Vehicle (OHV) Typing Standard Comment Form