simplify \frac{45a^{9}b^{4}}{\left(5ab^{2}\right)\left(3a^{4}b\right)}
First, we can multiply the terms in the denominator:
\( \left(5ab^{2}\right)\left(3a^{4}b\right) = 15a^{5}b^{3} \)
Therefore, the expression simplifies to:
\( \frac{45a^{9}b^{4}}{15a^{5}b^{3}} \)
Now, we can simplify further by dividing the coefficients and subtracting the exponents:
\( \frac{45}{15}a^{9-5}b^{4-3} = 3a^{4}b \)
So, the simplified expression is \( 3a^{4}b \)