simplifying expressions with exponents

[rage]

I have worked this problem through; however, I am not quite sure if I am correct.

[(2 * m)^3 * (3 * n)^-2] / [(3 * m * n^-1)^2]

= [(2m)^3 * (3n)^-2] / [(3mn^-1)^2)

= [(8m^3) * (1/9n^2)] / [(9m^2/n^2)]

= [ 8m^3/9n^2 / 9m^2/n^2 ]

Am I correct??

Another problem: If (x-3)(x+3)(x+3) / (x+3)(x+3)(x-3) does that equal x since everything is cancelled out or does it equal one?

 

[stapel]

1) You're correct, as far as you've gone. When dividing by a fraction, invert and multiply:

. . . . .[ 8m³ / 9n² ] / [ 9m² / n² ] = [ 8 m³ / 9n² ][ n² / 9m²]

Now simplify.

2) I'm not sure what you're saying here, especially since the question appears to begin with an incomplete sentence ("If this..." but no "then that"). On what basis could (x + 3)/(x + 3) be equal to "x"? But it would certainly be equal to "1", with the added proviso that x could not equal -3 (since this would cause division by zero in the original expression). This is because functions are not equivalent unless, among other things, they have the same domain.

Eliz.

 

[rage]

Final answer

So the final answer would be:

So the final answer would be: 8m^3n^2/81n^2m^3

 

[stapel]

So the final answer would be: 8m^3n^2/81n^2m^3

Can't you do some cancelling at this point...?

Eliz.