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Answer:
Step-by-step explanation:
You want the simplified form of (5b^1c^-5)^-3(4b^0a^2)^-5.
There are several useful rules of exponents here:
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
a^-b = 1/(a^b)
Simplifying the top-level exponents first, we have ...
[tex](5b^1c^{-5})^{-3}(4b^0a^2)^{-5}=(5^{-3}b^{1(-3)}c^{(-5)(-3)})(4^{-5}b^{0(-5)}a^{2(-5)})\\\\=(5^{-3}4^{-5})a^{-10}b^{-3+0}c^{15}=\dfrac{1}{5^34^5}a^{-10}b^{-3}c^{15}=\boxed{\dfrac{1}{128000}a^{-10}b^{-3}c^{15}}[/tex]
In terms of answer requirements:
n = 1/128000
r = -10
s = -3
t = 15