# Doublecheck reduction of rational expressions

1. Oct 7, 2016

### late347

1. The problem statement, all variables and given/known data
teacher gave me the correct solution which said that the result from him was as follows
$\frac{1}{a^2b^6}$

2. Relevant equations

original problem was as follows
$\frac{ (\frac{1}{a})^2*b^{-3}}{ ab^3 }$
3. The attempt at a solution

$\frac{\frac{1}{(a^2)b^3}}{ab^3}$

$= (\frac{1}{a^2b^3}) / (\frac{ab^3}{1})$

$= (\frac{1}{a^2b^3}) * \frac{1}{ab^3}$

$=\frac{1}{a^2b^3} ~~* ~~\frac{1}{a^1b^3}$

$=\frac{1}{a^3b^6}$

notice how there is the denominator $a^3b^6$

2. Oct 7, 2016

### Staff: Mentor

I agree with your answer, not your teacher's. Make sure that you and the teacher are both starting with the same expression.

3. Oct 7, 2016

### late347

yep on closer inspection... it looks like my teacher simply used rushed calculation, doing several things at the same time... and he made a typo because of that.

it look like he had a correct mid-result from an earlier calculation but forgot about it.