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\left(13a^{2}b^{3}-11c^{4}\right)\left(13a^{2}b^{3}+11c^{4}\right)
Rewrite 169a^{4}b^{6}-121c^{8} as \left(13a^{2}b^{3}\right)^{2}-\left(11c^{4}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).