Let's solve the given mathematical expression step-by-step: [tex]\(\left(2^{5/6} - 3^{1/2}\right) \div 12 / 3 \text{ of } 5^{2/3}\)[/tex].
First, we need to break down and calculate each component of the expression one by one.
1. Calculate [tex]\(2^{5/6}\)[/tex]:
[tex]\[ 2^{5/6} \approx 1.7817974362806785 \][/tex]
2. Calculate [tex]\(3^{1/2}\)[/tex] (which is the square root of 3):
[tex]\[ 3^{1/2} \approx 1.7320508075688772 \][/tex]
3. Subtract [tex]\(3^{1/2}\)[/tex] from [tex]\(2^{5/6}\)[/tex]:
[tex]\[ 2^{5/6} - 3^{1/2} \approx 1.7817974362806785 - 1.7320508075688772 = 0.049746628711801355 \][/tex]
4. Divide 12 by 3:
[tex]\[ 12 / 3 = 4 \][/tex]
5. Divide the result from step 3 by the result from step 4:
[tex]\[ \frac{0.049746628711801355}{4} = 0.012436657177950339 \][/tex]
6. Calculate [tex]\(5^{2/3}\)[/tex]:
[tex]\[ 5^{2/3} \approx 2.924017738212866 \][/tex]
7. Multiply the result from step 5 by [tex]\(5^{2/3}\)[/tex]:
[tex]\[ 0.012436657177950339 \times 2.924017738212866 \approx 0.03636500619239916 \][/tex]
Thus, the final result of the given expression [tex]\(\left(2^{5/6} - 3^{1/2}\right) \div 12 / 3 \text{ of } 5^{2/3}\)[/tex] is approximately:
[tex]\[ \boxed{0.03636500619239916} \][/tex]
