To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

\(\displaystyle 50\div(3+2)^2+5\)

\(\displaystyle 50\div(5)^2+5\)

Next, we evaluate the exponents:

\(\displaystyle 50\div25+5\)

Next, we complete the multiplication and division from the left to the right of the expression:

\(\displaystyle 2+5\)

Finally, we complete the addition:

\(\displaystyle 2+5 = 7\)

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

\(\displaystyle 3 + 2\cdot (4+1) - 5\)

\(\displaystyle 3 + 2\cdot (5) - 5\)

Next, we complete the multiplication:

\(\displaystyle 3 + 10 - 5\)

Finally, we evaluate the addition and subtraction from left to right in the expression:

\(\displaystyle 13 - 5 = 8\)

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

\(\displaystyle 50\cdot (3+7)^2\div25-27\)

\(\displaystyle 50\cdot (10)^2\div25-27\)

Next, we evaluate the exponents:

\(\displaystyle 50\cdot 100 \div25-27\)

Next, following PEMDAS, we evaluate the multiplication and division from left to right in the expression:

\(\displaystyle 5000 \div25-27\)

\(\displaystyle 200-27\)

Finally, we evaluate the subtraction:

\(\displaystyle 200-27 = 173\) 

First, work from left to right completing multiplication and division, then work from left to right completing addition and subtraction. 

\(\displaystyle 17+(2\cdot 4)-(6/2)\)

\(\displaystyle 17+8-3=22\)

Since \(\displaystyle 180 ^{\circ } = \pi \textrm{ rad}\), we can convert as follows:

\(\displaystyle \frac{7\pi }{2 5} \cdot \frac{180}{\pi } = \frac{7 }{ 5} \cdot \frac{36}{1 } =50.4^{\circ }\)

A fraction bar in an expression acts as both a division symbol and a grouping symbol, so we evaluate the numerator first. Within the numerator, there is a multplication, a subtraction, and an addition, so, by order of operations, we multiply first. Addition and subtraction are carried out right to left; the subtraction is left of the addition, so we subtract next, then add. Finally, we divide the numerator by the denominator.

In summary: Multiply, subtract, add, divide

By order of operations, always carry out any operations within parentheses first; this is the addition.  This removes the parentheses; what remains is a square, a multiplication, and a division. Since there are no more grouping symbols, square next. The multiplication is done next, as multiplications and divisions are performed in left-to-right order.

In summary: Add, square, multiply, divide

By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a subtraction. This is the correct order in the absence of grouping symbols.

In summary: Add, square, multiply, subtract

The order of operations is parenthesis, exponents, multiplication, division, addition, subtraction (PEMDAS).

\(\displaystyle 4+2x-1(5^2* 3)\)

First, we will evaluate the parentheses. Within the parentheses, we need to solve the exponent, then multiply,

\(\displaystyle 4+2x-1(25* 3)\)

\(\displaystyle 4+2x-1(75)\)

Now that the parenthesis is evaluated, we need to multiply.

\(\displaystyle 4+2x-75\)

Finally, we add and subtract. We can arrange the terms in any order.

\(\displaystyle 2x+4-75\)

\(\displaystyle 2x-71\)

Recall the order of operations. PEMDAS indicates that first parentheses, then exponents, then multiplication and division, followed by addition and subtraction, should be completed. We follow this process with this problem. 

\(\displaystyle 3(3 + 2)^{2} = 3(5)^{2} = 3(25) = 75\)