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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.

NWCG Latest Announcements

NWCG Equipment Technology Committee Releases Safety Warning: 24-001 Stihl Chainsaw Toolless Fuel Cap Spill Prevention

Date: November 14, 2024
Contact: Equipment Technology Committee

The Equipment Technology Committee (ETC) has released Safety Warning: 24-001 Stihl Chainsaw Toolless Fuel Cap Spill Prevention. Misaligned toolless fuel caps on Stihl chainsaws have led to recurring fuel spillage, fuel ignition, and burn injuries during wildland fire management operations.

This Safety Warning is intended to highlight the details and recommended procedures for the installation of a Stihl chainsaw toolless fuel cap, as well as how to identify and correct a misaligned, damaged, or broken fuel cap to help prevent fuel spillage.

References:

NWCG Safety Warning: 24-001 Stihl Chainsaw Toolless Fuel Cap Spill Prevention

Advertencia de equipos 24-001: Prevención de derrames de la tapa de combustible sin herramientas de la motosierra Stihl

NWCG Alerts

The Incident Position Standards and Next Generation Position Task Book are now available for Equipment Time Recorder (EQTR)

Date: November 13, 2024
Contact: Incident Business Committee

NWCG is excited to announce that the NWCG Incident Position Standards for Equipment Time Recorder, PMS 350-51 and NWCG Position Task Book for Equipment Time Recorder (EQTR), PMS 311-51 are now available.

The Performance Support Package, which for EQTR, includes the Incident Position Standards and Next Generation Position Task Book were developed through the Incident Performance and Training Modernization (IPTM) effort. The Performance Support Package will support trainees, those qualified in the position, and evaluators.

References:

NWCG Equipment Time Recorder Position Page

NWCG Incident Position Standards for Equipment Time Recorder, PMS 350-51

NWCG Position Task Book for Equipment Time Recorder (EQTR), PMS 311-51

The Incident Position Standards and Next Generation Position Task Book are now available for Personnel Time Recorder (PTRC)

Date: November 13, 2024
Contact: Incident Business Committee

NWCG is excited to announce that the NWCG Incident Position Standards for Personnel Time Recorder, PMS 350-53 and NWCG Position Task Book for Personnel Time Recorder (PTRC), PMS 311-53 are now available.

The Performance Support Package, which for PTRC, includes the Incident Position Standards and Next Generation Position Task Book were developed through the Incident Performance and Training Modernization (IPTM) effort. The Performance Support Package will support trainees, those qualified in the position, and evaluators.

References:

NWCG Personnel Time Recorder Position Page

NWCG Incident Position Standards for Personnel Time Recorder, PMS 350-53

NWCG Position Task Book for Personnel Time Recorder (PTRC), PMS 311-53

NWCG Risk Management Committee Releases Safety Bulletin: 24-001 Use of Respirators on Wildland Fires

Date: November 7, 2024
Contact: Risk Management Committee

The Risk Management Committee (RMC) has released Safety Bulletin: 24-001 Use of Respirators on Wildland Fires. As wildland fire respirators are available through several established vendors, wildland fire personnel need to understand regulations and limitations of respirator use in the workplace.

Safety Bulletin 24-001 outlines the following topics regarding respirator use for wildland fires:

  • Requirements for Respirator Use
  • Voluntary Respirator Use
  • Current Respirator Options
  • Unknown Risks of Respirator Use

This bulletin also provides mitigation recommendations to help reduce smoke exposure for wildland firefighting efforts.

References:

NWCG Safety Bulletin: 24-001 Use of Respirators on Wildland Fires

NWCG Smoke Management Guide for Prescribed Fire, PMS 420-3

VIDEO: Protecting Wildfire Personnel from Smoke - How Incident Management Teams Address Smokes Risks

VIDEO: Smoke, Knowing the Risks