The rules of exponents that apply here are ...
[tex]a^{b}\cdot a^{c}=a^{(b+c)}\\a^{-b}=\dfrac{1}{a^b}\\ \left(a^{b}\right)^{c}=a^{(b\cdot c)}[/tex]
1.
[tex]\displaystyle \left(\frac{4^{7}}{5^{2}}\right)^{3}=\frac{4^{(7\cdot 3)}}{5^{(2\cdot 3)}}\\\\=\frac{4^{21}}{5^{6}}[/tex]
2.
[tex]\displaystyle \frac{9^{2}}{9^{7}}=9^{(2-7)}=9^{-5}\\\\=\frac{1}{9^5}[/tex]
3.
[tex]\displaystyle \frac{6^{-3}}{6^{5}}=6^{(-3-5)}=6^{-8}\\\\=\frac{1}{6^8}[/tex]
