Question Regarding Negative Exponents: Simplify(2m/3n)^-3

[kitkatattack]

This is my first time using this website. I was was wondering for further reference on how to simplify an expression like this.

[imath](2m/3n)^-3[/imath]

The -3 is an exponent. As I said above, I just created an account and have no idea how to write through Latex! Sorry for the inconvinience.

- Kat ?

 

[stapel]

This is my first time using this website. I was was wondering for further reference on how to simplify an expression like this.

[imath]\left(\dfrac{2m}{3n}\right)^{-3}[/imath]

I suspect that, by "simplify", they mean "apply the exponent everywhere, and do any multiplication or cancellation that you can".

The minus exponent means that the terms in the fractional form are on the wrong side of the fraction line, so an immediate simplification is:

[imath]\qquad \left(\dfrac{3n}{2m}\right)^{3}[/imath]

Then cube everything inside, nothing that [imath]3^3 = 27[/imath] and [imath]2^3 = 8[/imath].

 

[lookagain]

[imath](2m/3n)^-3[/imath]

When written in horizontal style, the 3n needs to be inside grouping symbols,
and you can use the "^" symbol for exponentiation in general, as in x^2.
To achieve the first exponentiation in this case, I used "^ { - 3 }" but without
the spaces.

[imath][2m/(3n)]^{-3} \ = [/imath]

[imath][3n/(2m)]^{3} \ = [/imath]

[imath](3n)^3/(2m)^3 \ = [/imath]

[imath]3^3n^3/(2^3m^3) \ = [/imath]

[imath]27n^3/(8m^3) [/imath]