I need to simplify this without using a calculator.

(3b^4c^-1)(2b^-7c^-8)

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42b^-5c^4

Here's my try at it:

3x2 (b^4)(b^-7) (c^-1)(c^-8)

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42 (b^-5) (c^4)

6 b^-3 c^-9

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42 b^-5 c^4

1 b^2

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7 c^13

^ This symbol indicates an exponent.