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\frac{a^{2}b^{2}c^{2}}{\left(ab\right)^{3}c}
Expand \left(bc\right)^{2}.
\frac{a^{2}b^{2}c^{2}}{a^{3}b^{3}c}
Expand \left(ab\right)^{3}.
\frac{c}{ab}
Cancel out ca^{2}b^{2} in both numerator and denominator.
\frac{a^{2}b^{2}c^{2}}{\left(ab\right)^{3}c}
Expand \left(bc\right)^{2}.
\frac{a^{2}b^{2}c^{2}}{a^{3}b^{3}c}
Expand \left(ab\right)^{3}.
\frac{c}{ab}
Cancel out ca^{2}b^{2} in both numerator and denominator.