How do you simplify .(a/b^3)^-3?

Sep 22, 2015

Have a look:

Explanation:

You can consider that your negative cube is going to be applied to both numerator and denominator.
So you get:

${\left(\frac{a}{b} ^ 3\right)}^{-} 3 = \frac{{\left(a\right)}^{-} 3}{{\left({b}^{3}\right)}^{-} 3} =$
you now use the rule of exponents where ${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$ to get:
${a}^{-} \frac{3}{{b}^{-} 9}$

At this point you can use (although I am not sure about the usefulness of it) the idea that a negative exponent sends your base to another "floor"; so if, say, $a$ is at the numerator it can go downstairs to the denominator and viceversa.
In your case you can write:
${a}^{-} \frac{3}{{b}^{-} 9} = {b}^{9} / {a}^{3}$