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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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ETC Equipment Bulletin: 25-003 Flame-Resistant Shirt Survey

Date: June 12, 2025
Questions?  Please contact:
Equipment Technology Committee

The U.S. Forest Service National Technology and Development Program (NTDP) is seeking input on the Forest Service-designed flame-resistant (FR) shirt, currently available through the National Interagency Support Cache system and FedMall.

NTDP is conducting a product review to improve future FR shirt designs. As part of this effort, a short survey is now open for federal employees who have worn any of three recent FR shirt models. Feedback will guide design improvements to better meet the needs of wildland firefighters.

To comply with the Paperwork Reduction Act, responses are limited to federal employees. The survey is open through September 12, 2025. 

References:

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ETC Equipment Bulletin: 25-003

NEW! S-130, Firefighter Training (Blended) Now Available

Date: June 10, 2025
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The S-130, Firefighter Training (Blended), equips new wildland firefighters with essential skills through a mix of online learning and hands-on training. The course features a required online component and an instructor-led exercise, reinforcing online concepts with practical performance-based training.

The course builds competencies in wildland fire operations, safety, and equipment use, applicable across various operational environments. Both the online component and instructor-led field exercise must be completed to receive a certificate of completion. Students are required to finish the prerequisite S-190, Introduction to Wildland Fire Behavior, before enrolling in S-130, Firefighter Training (Blended).

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EMC Memo 25-001: Interim Rapid Extraction Module (REMS) Training and Qualification Requirements

Date: June 3, 2025
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The Emergency Medical Committee has issued interim guidance for Rapid Extraction Module Support (REMS) teams. Until further notice, Type I and II REMS teams must designate a team leader qualified at Firefighter Type 1 Squad Boss (FFT1) or higher. This temporary change replaces the Single Resource Boss (SRB) requirement, which is currently not feasible due to administrative barriers.

This memorandum does not include any other changes to the NWCG Standards for Rapid Extraction Module Support, PMS 552. This interim change takes effect immediately and will remain in place until further notice.

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Equipment Bulletin 25-002: Chaps, Chain Saw, M-2020, Nonconformities Affecting Use, Appearance, and Serviceability

Date: June 2, 2025
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The Equipment Technology Committee issued Equipment Bulletin: 25-002 to address a manufacturing nonconformity affecting Forest Service specification, 6170-4K Chain Saw Chaps. The issue applies to chaps manufactured in 2024 and 2025 and distributed through FedMall. These chaps may have incorrectly bound edges that expose inner protective layers.

Independent purchasers should inspect all chain saw chaps received from FedMall beginning in 2024, prior to use. Review the full Equipment Bulletin: 25-002 for inspection criteria and recommended actions.

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