Negative exponent

[dbush]

I'm back trying to help my son. I am trying to work a problem so I can better explain to him. The problem is
(5r^-2)^-2
_______
(2r³)²

I started with the power of a power and got here

5^-2r^4
_____
2²r⁶

Now what? Can you help? Many thanks

 

[pka]

5^-2r^4
_____
2²r⁶
Now what? Can you help?

\(\displaystyle \dfrac{5^{-2}r^4}{2^2r^6}=\dfrac{1}{100r^2}\) because \(\displaystyle {5^{-2}r^4}=\dfrac{r^4}{25}\).

 

[dbush]

Thank you. You are very helpful as always. Until next time...