Sure, let's evaluate the given expression step by step:
Given expression:
[tex]\[
\frac{\sqrt[4]{4000} \times 75.9}{5.61 \times 4.39}
\][/tex]
1. Calculate the fourth root of 4000:
To find the fourth root of [tex]\( 4000 \)[/tex], we need to find a number [tex]\( x \)[/tex] such that [tex]\( x^4 = 4000 \)[/tex]. The fourth root of [tex]\( 4000 \)[/tex] is approximately:
[tex]\[
\sqrt[4]{4000} \approx 7.9527
\][/tex]
2. Multiply the fourth root of 4000 by 75.9:
Next, we multiply [tex]\( 7.9527 \)[/tex] by [tex]\( 75.9 \)[/tex]:
[tex]\[
7.9527 \times 75.9 \approx 603.6105
\][/tex]
3. Calculate the product of the denominators [tex]\( 5.61 \)[/tex] and [tex]\( 4.39 \)[/tex]:
We multiply [tex]\( 5.61 \)[/tex] by [tex]\( 4.39 \)[/tex]:
[tex]\[
5.61 \times 4.39 \approx 24.6279
\][/tex]
4. Divide the result of the numerator by the result of the denominator:
Finally, we divide [tex]\( 603.6105 \)[/tex] by [tex]\( 24.6279 \)[/tex]:
[tex]\[
\frac{603.6105}{24.6279} \approx 24.5092
\][/tex]
Hence, the evaluated result of the expression is approximately:
[tex]\[
\frac{\sqrt[4]{4000} \times 75.9}{5.61 \times 4.39} \approx 24.5092
\][/tex]
