Question

Help me please I can't get the final step​

Answer 1

`\displaystyle m=(2)/(3),\ n=(4)/(3)`

Step-by-step explanation:

Dimensional Analysis

It's given the relation between quantities A, B, and C as follows:

`\displaystyle A=(3)/(2)B^mC^n`

and the dimensions of each variable is:

`A=L^2T^2`

`B=LT^(-1)`

`C=LT^2`

Substituting the dimensions into the relation (the coefficient is not important in dimension analysis):

`\displaystyle L^2T^2=\left(LT^(-1)\right)^m\left(LT^2\right)^n`

Operating:

`L^2T^2=\left(L^mT^(-m)\right)\left(L^nT^(2n)\right)`

`L^2T^2=L^(m+m)T^(-m+2n)`

Equating the exponents:

`m+n=2`

`-m+2n=2`

Adding both equations:

`3n=4`

Solving:

`n=4/3`

`m=2-4/3=2/3`

Answer:

`\mathbf{\displaystyle m=(2)/(3),\ n=(4)/(3)}`