Skip to main content

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

2025 Updates to the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1

Date: February 4, 2025
Contact: Incident and Position Standards Committee

The NWCG Incident and Position Standards Committee has updated the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1. 

These updates address changes to incident position names and requirements for qualification, training, and experience. Updates related to the implementation of Complex Incident Management (CIM) are also included.  

The NWCG Wildland Fire Position Qualification Flowchart, PMS 308 has also been updated to reflect the recent changes.

References:

NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1

NWCG Wildland Fire Position Qualification Flowchart, PMS 308

NWCG Memo: 2025-01 January 2025 Updates to the NWCG Standards for Wildland Fire Positions Qualifications, PMS 310-1

NWCG Equipment Technology Committee Releases Safety Warning: 25-001 Non-specification fire shelters

Date: January 15, 2025
Contact: Equipment Technology Committee

The Equipment Technology Committee (ETC) has released Safety Warning: 25-001 Non-specification fire shelters. Non-specification fire shelters claiming to meet Forest Service (FS) fire shelter specification 5100-606 were first found in February of 2023. As of September 2024, non-specification shelters are again being advertised and sold on the open market.

This Safety Warning outlines details and recommended procedures to purchase FS specification shelters made with materials and components that meet performance criteria and toxicity testing requirements outlined in FS Specification 5100-606. 

For additional information on identifying non-specification shelters, please view ETC Safety Warning 23-01.

References:

ETC Safety Warning 25-001: Non-specification fire shelters

NWCG Equipment Technology Committee

ETC Safety Warning 23-01

Paul Gleason Lead by Example Awards

Date: January 14, 2025
Contact: Leadership Committee

The NWCG Leadership Committee has awarded the 2023 Paul Gleason “Lead By Example” awards to individuals in the categories of Initiative and Innovation, Mentoring and Teamwork, and Motivation and Vision, as well as a Lifetime Achievement Award.

Congratulations to the awardees:

  • Sam Bowen, Superintendent of the Mark Twain Veteran Crew with the U.S. Forest Service.
  • Greg Titus, Zone Fire Management Officer for the St. Marks National Wildlife Refuge with U.S. Fish and Wildlife Service.
  • Renae Crippen, Manager of the Blue Mountain Interagency Dispatch Center with the U.S. Forest Service.
  • Eric Carlson, Instructor with OMNA International.

References:

Paul Gleason Lead by Example Award

Wildland Fire Leadership Development Program

Interview with Paul Gleason

Updated NWCG Standards for Water Scooping Operations, PMS 518

Date: December 19, 2024
Contact: Water Scooper Operations Unit

The NWCG Standards for Water Scooping Operations, PMS 518 establishes the standards for dispatching, utilizing, and coordinating water scooping aircraft on interagency wildland fires. These standards should be used in conjunction with the NWCG Standards for Aerial Supervision (SAS), PMS 505, and any local, state, or geographic/regional water scooping plans.

References:

NWCG Standards for Water Scooping Operations, PMS 518