Sure, let's solve the given expression step-by-step:
[tex]$2\left\{[(18 \div 3)-(\sqrt{9})]+\left[(4+6) \div 2+(3)^3\right]\right\}$[/tex]
1. First, solve the expression inside the first set of parentheses, [tex]\((18 \div 3) - (\sqrt{9})\)[/tex]:
- [tex]\(18 \div 3 = 6\)[/tex]
- [tex]\(\sqrt{9} = 3\)[/tex]
Subtract these results:
- [tex]\(6 - 3 = 3\)[/tex]
So, [tex]\((18 \div 3) - (\sqrt{9}) = 3\)[/tex].
2. Next, solve the expression inside the second set of parentheses within the brackets, [tex]\((4+6) \div 2 + (3)^3\)[/tex]:
- [tex]\(4 + 6 = 10\)[/tex]
- [tex]\(10 \div 2 = 5\)[/tex]
- [tex]\((3)^3 = 27\)[/tex]
Add these results:
- [tex]\(5 + 27 = 32\)[/tex]
So, [tex]\((4+6) \div 2 + (3)^3 = 32\)[/tex].
3. Now, sum up the results of these two calculations:
- [tex]\(3 + 32 = 35\)[/tex]
4. Finally, multiply this sum by 2:
- [tex]\(2 \times 35 = 70\)[/tex]
Therefore, the final result of the given expression [tex]\(2\left\{[(18 \div 3)-(\sqrt{9})]+\left[(4+6) \div 2+(3)^3\right]\right\}\)[/tex] is [tex]\(\boxed{70}\)[/tex].
