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\frac{-3ab^{4}}{\left(-3\right)^{2}\left(b^{2}\right)^{2}}
Expand \left(-3b^{2}\right)^{2}.
\frac{-3ab^{4}}{\left(-3\right)^{2}b^{4}}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\frac{-3ab^{4}}{9b^{4}}
Calculate -3 to the power of 2 and get 9.
\frac{-a}{3}
Cancel out 3b^{4} in both numerator and denominator.
\frac{-3ab^{4}}{\left(-3\right)^{2}\left(b^{2}\right)^{2}}
Expand \left(-3b^{2}\right)^{2}.
\frac{-3ab^{4}}{\left(-3\right)^{2}b^{4}}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\frac{-3ab^{4}}{9b^{4}}
Calculate -3 to the power of 2 and get 9.
\frac{-a}{3}
Cancel out 3b^{4} in both numerator and denominator.