The order of operations dictates that any operations within grouping symbols, such as parentheses, be carried out first; in this expression. There are two expressions - an exponentiation (squaring) and an addition - that fall between the parentheses; by the order of operations, the squaring is carried out, then the addition.

This leaves a multiplication, a division, and a subtraction. Multiplication and division have precedence over subtraction; since the multiplication appears first in left-to-right order, the multiplication is carried out next. This makes multiplication the correct response.

The order of operations dictates that the exponentiation (squaring) be carried out first. The multiplication and the division come next, in left-to-right order; since the multiplication appears to the left, this is worked first, followed by the division. Division is the correct response.

The order of operations dictates that any operations within grouping symbols is carried out first, going from the innermost symbols to the outermost symbols. The innermost symbols - the parentheses - flank an addition, so that operation is carried out first.

What remains within the outermost symbols - the brackets - are a multiplication and a division. Between the two, the one that is at left is carried out first; this means the multiplication is performed second, then the division is worked out third. 

Division is the correct answer.

Set  in the expression in the definition, then evaluate according to the order of operations:

Square first, remembering that the square of any number is nonnegative:

Add going left to right:

Set  and  in the expression in the definition, then evaluate according to the order of operations:

Multiplication and division take precedence over subraction; carry out the multiplication first, since it is the operation at left:

Divide next:

Now subtract:

Set  and  in the expression in the definition, then evaluate according to the order of operations:

By order of operations, carry out the exponentiation first:

The division is carried out next:

Now add:

The order of operations dictates that any operations within grouping symbols, such as parentheses, be carried out first; in this expression. There are two expressions - an exponentiation (squaring) and an addition - that fall between the parentheses; by the order of operations, the squaring is carried out, then the addition.

This leaves a multiplication, a division, and a subtraction. Multiplication and division have precedence over subtraction; since the multiplication appears first in left-to-right order, the multiplication is carried out next. This makes multiplication the correct response.

We refer to the order of operations to determine how to properly interpret a mathematical statement involving more than one operation. In this case, the operations involved are multiplication, exponentiation, addition, subtraction, and division, as can be seen from the reproduction of the expression below:

According to the order of operations, we focus our attention on the term with exponents first:

Next, we deal with the multiplication and division operations from left to right:

Finally, we deal with the addition and subraction operations from left to right:

Hence, the correct answer to the evaluation of the given expression is .

All we need to do is remember the quotient rule for exponents.

We apply this to each term and we get the following.

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". 

25 *( 47 + 72 + 19²)/12 + 65 =

25 * (47 + 72 + 361) / 12 + 65 =

25 * ( 480) / 12 + 65 =

12000 / 12 + 65 =

1000 + 65 = 1065