Solve [(136-sqrt(144)):2³×2-1]÷15: Complete Order of Operations

To solve the problem $[(136-\sqrt{144}):2^3\cdot2-1]:(3\cdot5) =$, we need to apply the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Start by calculating the expression inside the innermost parentheses:

• First, evaluate the square root: $\sqrt{144} = 12$. Substitute back into the expression, giving us $(136 - 12)$.

• Subtract: $136 - 12 = 124$.

• The expression now becomes $[124:2^3\cdot2-1]:(3\cdot5)$.

Next, handle the exponents:

• Calculate $2^3 = 8$.

Substitute back, and the expression becomes:

• $[124:8\cdot2-1]:(3\cdot5)$

Now perform the operations inside the square brackets:

• Perform the division: $124:8 = 15.5$.

• Next, multiply: $15.5 \cdot 2 = 31$.

• Subtract 1: $31 - 1 = 30$.

The expression simplifies to:

• $30:(3\cdot5)$

Simplify further by handling the multiplication in the denominator:

• Calculate $3 \cdot 5 = 15$.

Finally, divide:

• $30:15 = 2$.

Thus, the answer is $2$.