Problem 87 - Elementary Algebra

Question

For exercises 85-88, use a calculator to evaluate. If the calculator has parentheses, use them. $$ 4+(9-1)^{2} $$

Step-by-Step Solution

Answer

68

Step 1: Identify the Operation Inside the Parentheses

First, solve the operation inside the parentheses. In this case, it is (9-1).

Step 2: Calculate Inside the Parentheses

Evaluate (9-1): 9-1 = 8.

Step 3: Substitute and Simplify

Replace the parentheses with the result from the previous step. The expression now is 4 + 8^2.

Step 4: Square the Result

Calculate the square of 8: 8^2 = 64.

Step 5: Final Addition

Add the result of the squaring operation to 4: 4 + 64 = 68.

Key Concepts

Parentheses

Parentheses are symbols used to group parts of a mathematical expression. Solving expressions within parentheses first is crucial for accuracy. Consider the expression 4 + (9-1)^2.
Here, the operation inside the parentheses (9-1) must be handled before anything else. This follows the order of operations rule, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
By doing so, we simplify the expression step-by-step, avoiding any mistakes. So remember, whenever you see parentheses, take care of them first!

Exponents

Exponents are a way to express repeated multiplication of a number by itself. In the expression 4 + (9-1)^2, after solving the parentheses, we get 4 + 8^2.
Here, 8 is raised to the power of 2. This means multiplying 8 by itself: 8 × 8, which equals 64.

Handling exponents can change the value of an expression significantly. It simplifies to realize that exponents represent power and can change a base number quite a bit. This can make seemingly complex expressions much easier to handle once exponents are understood!

Basic Arithmetic

Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division. To solve our original expression 4 + (9-1)^2, we use several of these operations.
Firstly, we subtract inside the parentheses (9-1) = 8.
Next, we deal with the exponent: 8^2 = 64.
Finally, we add the result to the remaining number outside the parentheses: 4 + 64 = 68.
Breaking down each step helps in handling even more complex expressions. Remembering and applying basic arithmetic rules can make problem-solving straightforward and understandable!