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Chapter 2: Problem 88

Perform the indicated operations. $$3\left(4^{2}\right)+10 \div 5$$

Short Answer

Expert verified
The result of the operation is 50.

Step by step solution

01

Simplify the Exponent

First, calculate the exponent in the expression. Evaluate \(4^2\), which is \(4\times4=16\). This will replace \(4^2\) in the equation.
02

Distribute the Multiplication

Next, multiply the result from Step 1 by 3. Thus, compute \(3 \times 16\), which equals \(48\).
03

Evaluate the Division

Now tackle the division portion of the expression. Calculate \(10 \div 5\), which simplifies to \(2\).
04

Add the Results

Finally, add the results from Step 2 and Step 3 to complete the operations. Compute \(48 + 2\), which equals \(50\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Exponents
Exponents are a mathematical way to represent repeated multiplication. When you see an expression like \(4^2\), it means that the number 4 is multiplied by itself. Specifically, \(4^2=4 \times 4\), which equals 16.
Understanding the placement of exponents is vital. The number that is raised to the power, in this case 4, is called the "base." The small number written to its upper right, 2 in this scenario, is the "exponent."
Here's a simple process to follow when dealing with exponents:
  • Identify the base and exponent.
  • Multiply the base by itself as many times as indicated by the exponent.
  • Replace the exponential term with the calculated value in your expression.
In our exercise, \(4^2\) was simplified right away, making it easier for future steps.
Division and Multiplication Clarified
In mathematical operations, division and multiplication are of the same precedence level. This means you should solve them as they appear from left to right in the expression.
For example, in the expression \(3(16) + 10 \div 5\), multiplication happens first because the expression after applying exponentials becomes \(3 \times 16\).
Here's the guideline for tackling these operations:
  • Process them from left to right.
  • Prioritize multiplication and division over addition and subtraction.
In this context, after simplifying \(3 \times 16\) to get 48, you move to \(10 \div 5\). The division results in 2. So, 48 from the previous multiplication and 2 from the division line us up perfectly for addition.
Addition and Subtraction Simplified
Addition and subtraction are the final steps in operation order. Once the exponents, multiplication, and division parts are handled, we can easily proceed to addition or subtraction.
In our exercise, after computing the multiplication and division results, what's left is to add them together. This is the step where you combine the results achieved earlier.
Steps in handling addition and subtraction:
  • Proceed after completing higher precedence operations such as exponents, multiplication, and division.
  • Combine the terms from left to right.
In the problem, we added 48 and 2, obtained from prior calculations, resulting in the final answer of 50. Doing additions and subtractions last helps to ensure no error in order precedence.

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