Problem 91 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ (-6)^{2} \cdot 12 \div 3-4 $$

Step-by-Step Solution

Answer

140

Step 1 - Evaluate the exponent

First, calculate \( (-6)^2 \). \( (-6)^2 = 36 \).

Step 2 - Multiply the result by 12

Next, multiply the result from step 1 by 12. \( 36 \times 12 = 432 \).

Step 3 - Divide by 3

Now, take the result from step 2 and divide it by 3. \( 432 \div 3 = 144 \).

Step 4 - Subtract 4

Finally, subtract 4 from the result of step 3. \( 144 - 4 = 140 \).

Key Concepts

Order of Operations

When solving any algebra problem, it's crucial to follow the order of operations. This ensures that the solution is consistent and correct.

The order of operations can be remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. According to PEMDAS, you should perform calculations in the following order:

• First, handle anything inside parentheses.
• Next, calculate the exponents.
• Then, perform multiplication and division from left to right.
• Finally, conduct addition and subtraction from left to right.

By following PEMDAS, you can systematically work through any arithmetic or algebraic expression correctly.

Exponents

Exponents are a way to represent repeated multiplication of a number by itself. For instance, \((-6)^2\) means you multiply -6 by itself: \(-6 \times -6\).

When calculating exponents, remember that when the base (the number being raised to the power) is negative and the exponent is even, the result will be positive. Conversely, if the exponent is odd, the result will be negative. For example:

• \((-6)^2 = 36\) because -6 multiplied by -6 gives a positive result.

In our exercise, the exponentiation was the first operation calculated.

Multiplication and Division

Multiplication and division should be performed from left to right as they appear in the expression.

In our example, after solving the exponent, the multiplication and division steps were as follows:

• First, multiply the result of \((-6)^2\) by 12: \(36 \times 12 = 432\)
• Next, divide the result by 3: \(432 \div 3 = 144\)

Always remember to do these operations sequentially and from left to right to ensure the correct solution.

Subtraction

Subtraction is usually the last step in an expression according to PEMDAS.

This means you perform all other operations first before you subtract. In our exercise, after calculating the exponent, multiplication, and division, the final step was subtraction:

• Subtract 4 from the result of the division step: \(144 - 4 = 140\)

Always verify if there are any additional operations left before performing subtraction to avoid mistakes.