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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.

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Incident Position Standards and the Next Generation Position Task Books Now Available for DMOB, DOCL, and RESL

Date: February 28, 2025
Contact: Incident Operations Subcommittee

NWCG is excited to announce that Incident Position Standards and the Next Generation Position Task Books are now available for Demobilization Unit Leader (DMOB), Documentation Unit Leader (DOCL), and Resources Unit Leader (RESL).

The Performance Support Packages for these positions, including a job aid for RESL, were developed as part of the Incident Performance and Training Modernization (IPTM) effort. These resources support trainees, qualified personnel, and evaluators in their respective roles.

Any changes to qualification pathways will take effect with the next update of the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1.

References:

NWCG Demobilization Unit Leader Position Page 

NWCG Documentation Unit Leader Position Page 

NWCG Resources Unit Leader Position Page 

Next Generation Position Task Book and Updated Incident Position Description Now Available for Operations Section Chief Complex

Date: February 27, 2025
Contact: Incident Operations Subcommittee

NWCG is excited to announce that Operations Section Chief Complex (OSCC) has a Next Generation NWCG Position Task Book for Operations Section Chief Complex (OSCC), PMS 311-108 and an updated Incident Position Description.

These resources support trainees, qualified personnel, and evaluators in their respective roles.

References:

NWCG Operations Section Chief Complex Position Page 

NWCG Operations Section Chief Complex Incident Position Description 

NWCG Position Task Book for Operations Section Chief Complex (OSCC), PMS 311-108 

2025 NWCG Incident Response Pocket Guide (IRPG), PMS 461, Now Available

Date: February 27, 2025
Contact: Incident Operations Subcommittee

NWCG is excited to announce that the 2025 NWCG Incident Response Pocket Guide (IRPG), PMS 461, is now available. Visit NWCG's website to learn about the major updates and changes in the 2025 version of the IRPG. The NWCG Guia de Respuesta de Incidente de Bolsillo (GRI), PMS 461-ES is available electronically and will be available from Great Basin Cache by early summer 2025.

All hard copy materials, including the IRPG, are ordered through the Great Basin Cache (GBK). Information on the ordering process can be found in the National Fire Equipment System (NFES) Catalog.

References:

2025 IRPG Information 

NWCG Incident Response Pocket Guide (IRPG), PMS 461 

NWCG Guia de Respuesta de Incidente de Bolsillo (GRI), PMS 461-ES 

NWCG NFES Catalog - Part 2: Publications, PMS 449-2 

2025 Professional Reading Program

Date: February 18, 2025
Contact: Wildland Fire Leadership Development Program (WFLDP)

The Wildland Fire Leadership Development Program is announcing the 2025 Professional Reading list! The goal of the annual reading list is to promote the reading and discussion of the books throughout the year.

The five books chosen for this year are: Surf When You Can by Brett Crozier, Man’s Search for Meaning by Viktor E. Frankl, Elephant Company by Vicki Constantine Croke, Simply Managing by Henry Mintzberg, and Chop Wood Carry Water by Joshua Metcalf.

References:

Professional Reading Program