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Chapter 1: Problem 97

Simplify each expression. $$2+4^{2}$$

Short Answer

Expert verified
The simplified expression is 18.

Step by step solution

01

Working Out the Exponent

The first thing to do is to carry out the exponent operation. Here, we have \(4^2\), which means '4 multiplied by itself 2 times'. This will give us 16.
02

Perform the Addition

Next, add the result of the exponent operation (16) to the remaining number in the expression. So, that's \(2 + 16\), which results in 18.

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Key Concepts

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

Exponentiation
Exponentiation is the mathematical operation involving numbers called bases and exponents (or powers). It represents repeated multiplication of a base by itself. In the expression \(4^2\), the base is 4, and the exponent is 2. Therefore, \(4^2\) means \(4 \times 4\), giving you 16.
Often, exponentiation is simplified before other operations when solving expressions.
Here are some key points:
  • The base is the number being multiplied.
  • The exponent tells us how many times to multiply the base by itself.
  • Exponentiation is a more concise way to express repeated multiplication.
Remember, correctly identifying and computing powers can greatly simplify your work with algebraic expressions.
Order of Operations
When simplifying mathematical expressions, it's important to follow the order of operations to ensure consistency and correctness. This is commonly remembered by the acronym PEMDAS:
  • Parentheses: Solve expressions inside parentheses first.
  • Exponents: Simplify exponents (powers and roots).
  • Multiplication and Division: Handle these operations from left to right.
  • Addition and Subtraction: Handle these from left to right.
In the exercise, after calculating \(4^2\) first, you moved on to addition (\(2 + 16\)), following the proper order of operations and achieving the answer 18.
Arithmetic Operations
Arithmetic operations are fundamental math skills that include addition, subtraction, multiplication, and division.
In simplifying expressions, understanding these operations is crucial.
The original exercise required adding the result of an exponent calculation to another number. Here are the basics:
  • Addition: Combining two numbers to get a sum. In our example, the numbers 2 and 16 were added.
  • Subtraction: Finding the difference between two numbers.
  • Multiplication: Repeated addition of a number.
  • Division: Splitting a number into equal parts.
Accurate arithmetic operations ensure that expressions are simplified correctly, leading to the right results.

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