Multiply the fractions \( \frac{43 \times 301^{90}}{5^{177} \times 2^{89} \times 6^{90}} \)

To multiply the fractions, we first simplify the expression given: \[ \frac{43 \times 301^{90}}{5^{177} \times 2^{89} \times 6^{90}} \] We can rewrite \(6^{90}\) as \( (2 \times 3)^{90} = 2^{90} \times 3^{90}\). Thus, we have: \[ \frac{43 \times 301^{90}}{5^{177} \times 2^{89} \times (2^{90} \times 3^{90})} \] Now, substituting this into the denominator gives us: \[ \frac{43 \times 301^{90}}{5^{177} \times 2^{89 + 90} \times 3^{90}} = \frac{43 \times 301^{90}}{5^{177} \times 2^{179} \times 3^{90}} \] At this point, the expression is simplified, but we can’t perform any further arithmetic without specific values or additional context for \(301^{90}\). Therefore, the final simplified result is: \[ \frac{43 \times 301^{90}}{5^{177} \times 2^{179} \times 3^{90}} \]