Evaluate : $45-[38-(60÷3-(6-9÷3)÷3\left)\right]$.

To evaluate an expression , we must first simplify the expression below the vinculum, then inside the small bracket , then inside the curly bracket , and finally inside the square bracket using the DMAS rule,

Thus, $45-[38-(60÷3-(6-9÷3)÷3\left)\right]$

$=45-[38-(60÷3-(6-3)÷3\left)\right]$
[Division in small bracket : $9÷3=3\text{inside}\left(\right)]$

$=45-[38-(60÷3-3÷3\left)\right]$

[Removing small bracket ]

$=45-[38-(20-1\left)\right]$

[Division in only brackets : $60÷3=20,3÷3=1$]

$=45-[38-19]$

[Removing curly bracket]

$=45-19$
[Removing square bracket]

$=26$

$\therefore$ The value of $45-[38-(60÷3-(6-9÷3)÷3\left)\right]$ is $26$.