Answer:
1/(8b^2a^8)
Step-by-step explanation:
The given expression can be simplified using the rules of exponents.
[tex]ba^4\times(2ba^4)^{-3}=\dfrac{ba^4}{(2ba^4)^3}=\dfrac{ba^4}{8(ba^4)^3}=\dfrac{1}{8(ba^4)^2}=\boxed{\dfrac{1}{8b^2a^8}}[/tex]
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The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
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Additional comment
It can be useful to think of an exponent as indicating repeated multiplication: 2^3 = 2×2×2, for example. Of course, the repeated multiplication can be nested: (4^2)^3 = (4^2)×(4^2)×(4^2) = (4×4)×(4×4)×(4×4) = 4^6
Numerator and denominator factors cancel in the usual way.
