(2b^4 c^-2)^5 (3b^-3 c^-4)^-2

(2b^4 c^-2)^5 (3b^-3 c^-4)^-2

Applying a rule of exponents that (a^m)ⁿ = a^m*n......we have.........

(2)^5 *( b^4)^5* (c^-2)^5 * (3)^-2 * (b^-3)^-2 * (c^-4)^-2

32 * b^20 * c^-10 * (1/9)  * b^6 * c^8

And using another rule that a^m * aⁿ  = a^m+n  ...... we have.......

(32)(1/9)(b^20)(b^6)(c^-10)(c^8) =

(32/9)*(b^26)(c^-2) =               ............... remember c^-2 = 1/c^2............

[32b^26 ] / [9c^2]