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The expression (4 b^{2} c^{-4})^{-5} (5 b^{2} a^{3})^{-4} equals na^rb^sc^t

The expression (4 b^{2} c^{-4})^{-5} (5 b^{2} a^{3})^{-4} equals na^rb^sc^t
where n, the leading coefficient, is: ____
and r, the exponent of a, is: ____
and s, the exponent of b, is: ____
and finally t, the exponent of c, is: ____
[NOTE: Your answers cannot be algebraic expressions.]
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1 Answer

(4 b^{2} c^{-4})^{-5} (5 b^{2} a^{3})^{-4}
 
= (4^{-5} b^{-10} c^{20})*(5^{-4} b^{-8} a^{-12})
 
= 4^{-5} 5^{-4} a^{-12} b^{-18} c^{20}
 
= n a^r b^s c^t 
 
n = 1/((4^5)(5^4))
 
r = -12
 
s = -18
 
t = 20