Remember the order of operations: PEMDAS

Start by simplifying what is found in the parentheses:

Next, simplify the exponents.

Next, take care of any multiplication and division.

Finally, add and subtract.

Recall the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

First, simplify the terms in the parentheses.

Next, simplify the exponents.

Next, simplify any multiplication and division.

Finally, simplify any addition and subtraction.

Simplify the following expression:

Recall PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This is our order of operations, the order we need to go in when simplifying mathematical expressions.

Let's begin with parentheses. We need to simplify the innermost parentheses first:

Next, we need to simplify the exponent on the 4. 

Now, we went through a lot there, but basically, by simplifying the 4 squared and then subtracting it from 16, we made the inside of our parentheses "0". When we multiplied the 4 through, everything within the parentheses canceled out, leaving us with just 12.

 So, our answer is 12

Recall the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Start by simplifying everything found in the parentheses.

Next, simplify the exponents.

Next, multiply and divide where indicated.

Finally, add and subtract.

Substitute 5 for  and 7 for :

By order of operations, square, then add, then subtract:

Substitute the value of each given variable in the expression, noting that the implied operation between  and  is multiplication:

In the order of operations, multiplication precedes addition, so multiply first. Multiply as if you were multiplying 12 by 7, then position the decimal point so that two digits (one in 1.2 plus one in 0.7) are to the right:

Now, 

Append a 0 to the 0.4, then subtract, lining up decimal points:

The result is negative, so

.

Recall that there are  pints in a gallon. Then, we can write the following equation to find the number of pints in  gallons.

 pints must be used to fill the jug.

Recall the order of operations. 

First, tackle the insides of the parentheses:

Next, take care of any exponents.

Next, simplify any multiplication and division.

Finally, simplify the addition and subtraction.

Substitute 7 for  and for in the expression to get

Evaluate according to the order of operations. Multiplication and division, worked in left-to-right order, take precedence over addition, so multiply first, as shown:

Divide next, as shown:

Finally, add:

,

the correct response.

Substitute and 9 for and in the expression:

Evaluate the numerator first. Since exponentiation takes precedence over addition in the order of operations, square 9 first:

Now, add as follows:

This fraction can be simplified by dividing both halves by 3:

Divide 25 by 3 to restate this as a mixed fraction:

, so

,

the correct value.