How Do You Simplify Dimensional Analysis Equations?

[Byeongok]

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

 

[cnh1995]

EDIT: Is it
[T]-3

yes.

 

[BOAS]

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 $\frac{1}{[T]^{2}} \frac{1}{[T]} = [T]^{-2 + -1} = [T]^{-3}$