How do you simplify the expression ((qr^2s)/(3r^4))^-3 using the properties?

May 15, 2017

See below.

Explanation:

Before we deal with the exponent, let's deal with the fraction.

We know that ${r}^{a} / {r}^{b} = {r}^{a - b}$

So, ${r}^{2} / {r}^{4} = \frac{1}{r} ^ 2$

The expression becomes:

${\left(\frac{q s}{3 {r}^{2}}\right)}^{-} 3$

When we have a negative power in the exponent, we flip the fraction.

${\left(\frac{3 {r}^{2}}{q s}\right)}^{3}$

Now we cube everything.

$\frac{27 {r}^{6}}{{q}^{3} {s}^{3}}$