The power rule states that $a \log_b c = \log_b c^a$. Applying this rule to the given expressions, we get:
(a) $\log _{10}\left(x^{2}-16\right)-\log _{10}(x+4)^3+\log _{10} x^2$
(b) $\log _{10}\left(x^{2}-16\right)-3\left[\log _{10}(x+4)+\log _{10} x^2\right]$
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