5^2*5^3
5^4
(5^2) ^1/2
4^3:2^3
2^2
6^4:2^4
3^2
3^-2
5^-3 * 5^4
4^-1/2
Just ask one question at a time please.
Also
The colons have not meaning.
I'll do the first one
\(\frac{5^2*5^3}{5^4}=\frac{5^{2+3}}{5^4}=\frac{5^{5}}{5^4}=5^{5-4}=5^1=5\)