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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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Updated NWCG Standards for Fire Unmanned Aircraft Systems Operations, PMS 515

Date: April 23, 2025
Questions?  Please contact:
Interagency Fire Unmanned Aircraft Systems Subcommittee

The NWCG Standards for Fire Unmanned Aircraft Systems Operations, PMS 515 standardizes processes and procedures for the interagency use of Unmanned Aircraft Systems (UAS), including pilot inspections and approvals. This updated publication provides the aviation community with standards to ensure UAS are used safely, effectively, and efficiently in support of fire management goals and objectives.

References:

NWCG Standards for Fire Unmanned Aircraft Systems Operations, PMS 515

NWCG National Interagency Aviation Committee

ETC Bulletin 25-001: Retrofitted Hot/Cold Beverage Kits - 2025 Field Season

Date: April 16, 2025
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Equipment Technology Committee

Due to spout failures and the associated risk of burn injuries, manufacturers have retrofitted the Hot/Cold Beverage Kits using a heat-shrinking band to secure the black spout at the insertion site. The updated kits feature a fluorescent label on each full kit assembly for easy identification. Catering units are encouraged to confirm the clear heat-shrinking bands are intact around each spout before filling.

ETC Bulletin 24-001 regarding Hot/Cold Beverage Kits has been archived and replaced by ETC Bulletin 25-001 for the 2025 season.

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NWCG Alerts

ETC-EB-25-001 Retrofitted Hot/Cold Beverage Kits

NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212, and Next Generation Position Task Book for Basic Faller Are Now Available

Date: April 14, 2025
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Hazard Tree and Tree Felling Subcommittee

The updated NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212, and NWCG Position Task Book for Basic Faller (FAL3), PMS 311-19 are now available.

The NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212 includes position standards designed to be used in conjunction with the Next Generation Position Task Book (Next Gen PTB). The Next Gen PTB for Basic Faller (FAL3) includes an evaluation guide with suggested rating elements to consider when assessing trainees.

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NWCG Standards For Wildland Fire Chainsaw Operations, PMS 212

NWCG Position Task Book for Basic Faller (FAL3), PMS 311-119

NWCG Basic Faller (FAL3)

RMC Memo 25-01: Summary of Updates to Safety Officer Positions

Date: April 9, 2025
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RMC Member Eric Fransted

The Risk Management Committee (RMC) serves as the position steward for all Safety Officer incident positions and continues to improve position standards, training, and naming conventions. The implementation of Complex Incident Management (CIM) required changes to position titles. RMC collaborated with the NWCG Incident Position Standards Committee (IPSC) to propose and implement these updates. 

References:

RMC Memo 25-01: Summary of Updates to Safety Officer Positions 

NWCG Position Catalog