How Do You Simplify Dimensional Analysis Equations?

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SUMMARY

The discussion focuses on simplifying the dimensional analysis equation [T]⁻²/[T]. The correct simplification is [T]⁻³, confirmed through the property of exponents where x⁽ᵃ⁾ x⁽ᵇ⁾ = x⁽ᵃ + ᵇ⁾. The participant initially attempted to express the equation as 1/[T]³, which is valid and leads to the same conclusion. The key takeaway is the application of exponent rules in dimensional analysis.

PREREQUISITES
  • Understanding of dimensional analysis in physics
  • Familiarity with exponent rules
  • Basic knowledge of units of measurement
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the properties of exponents in algebra
  • Learn more about dimensional analysis techniques
  • Explore examples of dimensional analysis in physics problems
  • Review unit conversion methods and their applications
USEFUL FOR

Students new to physics, educators teaching dimensional analysis, and anyone looking to strengthen their understanding of unit simplification in scientific equations.

Byeongok
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Homework Statement


Hello, I am new to physics and i was wondering what i should do for the following equation to simplify it.

Homework Equations


[T]-2/[T]

The Attempt at a Solution


I tried

1/[T]3
Which I'm not sure is possible when dimensional analyzing.

EDIT: Is it
[T]-3
 
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Byeongok said:
EDIT: Is it
[T]-3
yes.
 
Byeongok said:

Homework Statement


Hello, I am new to physics and i was wondering what i should do for the following equation to simplify it.

Homework Equations


[T]-2/[T]

The Attempt at a Solution


I tried

1/[T]3
Which I'm not sure is possible when dimensional analyzing.

EDIT: Is it
[T]-3

If you recall that ##x^{\alpha} x^{\beta} = x^{\alpha + \beta}## and that ##\frac{1}{[T]} = [T]^{-1}##, we can see that your answer is correct.

We have ##\frac{1}{[T]^{2}} \frac{1}{[T]} = [T]^{-2 + -1} = [T]^{-3}##
 
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