Hope I can be of assistance!
[tex]3^2b^2c^{-4}\cdot \:3^{-1}b^{-5}c^7 \ \textgreater \ \mathrm{Apply\:exponent\:rule}:\ \:a^b\cdot \:a^c=a^{b+c} [/tex]
[tex]3^{-1}\cdot \:3^2=\:3^{2-1}=\:3^1=\:3 \ \textgreater \ 3b^{-5}b^2c^{-4}c^7[/tex]
[tex]\mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c} \ \textgreater \ b^{-5}b^2=\:b^{2-5}=\:b^{-3}[/tex]
[tex]3b^{-3}c^{-4}c^7[/tex]
[tex]\mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c} \ \textgreater \ c^{-4}c^7=\:c^{-4+7}=\:c^3[/tex]
[tex]3b^{-3}c^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}: \:a^{-b}=\frac{1}{a^b} \ \textgreater \ b^{-3}=\frac{1}{b^3} \ \textgreater \ 3\cdot \frac{1}{b^3}c^3[/tex]
[tex]\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{1\cdot \:3c^3}{b^3}[/tex]
Finally
[tex]\mathrm{Apply\:rule}\:1\cdot \:a=a \ \textgreater \ \frac{3c^3}{b^3}[/tex]
Hope this helps!
