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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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2025-2026 Wildland Fire Leadership Campaign: "Leadership Levels" Now Available

Date: October 15, 2025
Questions? Please contact:
Leadership Committee

NWCG is excited to announce the release of the Leadership Committee’s 2025–2026 Leadership Campaign, themed “Leadership Levels.” This annual initiative offers all students of leadership and wildland fire management an opportunity to engage with essential leadership skills and knowledge needed to lead effectively in dynamic environments.

The campaign is structured into four quarters and may be completed at any time between October 1, 2025 -December 31, 2026. Leadership levels will be released quarterly.

Quarter One materials are now available on the Wildland Fire Leadership Development Program website and focus on Leadership Level 1, Follower (Self-Leadership).

References:

2025/2026 NWCG Leadership Campaign - Leadership Levels

Wildland Fire Leadership Development Program

Leadership Committee

Updated! L-280, Followership to Leadership (Instructor-led) Course

Date: October 3, 2024
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Leadership Committee

NWCG is pleased to announce the updated L-280, Followership to Leadership (Instructor-led) course is now available. L-280 is intended for operational personnel at the Firefighter Type 1 level, and for individuals pursuing Leadership Level 2, New Leader. 

This instructor-led course is a primer on leadership and the second formal course in the Wildland Fire Leadership Development Program. It helps emerging leaders build the confidence, skills, and mindset needed to lead effectively in high-risk environments. 

For more information about leadership development and available courses, visit the Leadership Committee Web Portal.

References:

L-280, Followership to Leadership (Instructor-led)

Wildland Fire Leadership Development Program

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Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use

Date: Sept 26, 2025
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Equipment Technology Committee 

The Equipment Technology Committee (ETC) has released Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use. This advisory recommends all pre-2006 fire shelters should be removed from service by January 1, 2026.

This advisory recommends firefighters and fire managers to:

  • Inspect fire shelters immediately
  • Replace and destroy any pre-2006 shelters (identified by white or pink insert label)
  • Order replacements as needed

For further details, please refer to the complete advisory. 

References:

Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use

NWCG Fire Inspection Flowchart, PMS 411-1

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NEW! S-219, Firing Operations (Blended) Now Available

Date: Sept 11, 2025
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Fuels Management Committee 

The S-219, Firing Operations (Blended) course is now available on the Wildland Fire Learning Portal. Developed through the Incident Performance and Training Modernization (IPTM) effort, this training supports individuals working towards Firing Boss, Single Resource (FIRB) incident qualifications.

This blended course combines online and instructor-led training to provide students with the knowledge and skills required to perform the duties of the FIRB, as described in the NWCG Incident Position Standards for Firing Boss, Single Resource, PMS 350-105.

Any changes to qualification pathways will take effect with the next update of the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1, scheduled for January 2026.

References:

S-219, Firing Operations (Blended)

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