I need to simplify this:

(2b^-7c^4)^4

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5^-1 b^2 c^6

Here's my attempt:

2^4 (b^7)^4 (c^4)^4

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.2 b^2 c^6

16 b^-28 c^16

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.2 b^2 c^6

80c^10

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b^30

Is this correct?

( ^ followed by a number represents an exponent)