Evaluate: \( 4.993^{1.893 / 9.621}+3.498^{9.621 / 1.893} \)

To evaluate the expression \( 4.993^{1.893 / 9.621}+3.498^{9.621 / 1.893} \), we will calculate each term separately. First, let’s find \( 4.993^{1.893 / 9.621} \): The exponent \( \frac{1.893}{9.621} \) is approximately \( 0.196 \). Therefore, we calculate: \[ 4.993^{0.196} \approx 1.607 \] Now, we calculate \( 3.498^{9.621 / 1.893} \): The exponent \( \frac{9.621}{1.893} \) is approximately \( 5.080 \). Therefore, we compute: \[ 3.498^{5.080} \approx 248.287 \] Now we add these two results together: \[ 1.607 + 248.287 \approx 249.894 \] Thus, the value of the expression \( 4.993^{1.893 / 9.621}+3.498^{9.621 / 1.893} \) is approximately \( \boxed{249.894} \).