Problem 9 - Algebra A Combined Function

Question

Evaluate. $$ 7^{2} $$

Step-by-Step Solution

Answer

49

Step 1: Understand the Expression

We are given the expression \( 7^2 \). This means we need to calculate the square of 7, which involves multiplying 7 by itself.

Step 2: Multiply the Base by Itself

To find \( 7^2 \), we multiply 7 by itself: \( 7 \times 7 \).

Step 3: Calculate the Product

Perform the multiplication: \( 7 \times 7 = 49 \).

Step 4: Verify the Result

Double-check the calculation: \( 7 \times 7 = 49 \) confirms that the computation is correct.

Key Concepts

Understanding Squares

When you come across the term "square" in mathematics, it is referring to a specific way of using exponents. The square of a number is essentially when a number is multiplied by itself. This is expressed in mathematical terms by raising that number to the power of two.

For example, the square of 7 is written as \(7^2\). This means you take the number 7 and multiply it by itself.

• The first step is to identify the base number, which, in this example, is 7.
• Next, recognize that the exponent or power (2 in this case) signifies taking the number and multiplying it by itself once.
• The result, in this case, of 7 multiplied by 7 gives us the square, which is 49.

Thinking about squares in this way helps simplify problems into more manageable steps.

Basics of Multiplication

Multiplication is one of the fundamental operations in math and is essentially repeated addition.

When you see a multiplication problem, like \(7 \times 7\), it means "seven taken seven times." Let's break this down.

• Start with your first number (here it's 7) and think of 7 groups of this number.
• If you list it out, you are summing up 7 + 7 + 7 + 7 + 7 + 7 + 7.
• The shortcut is multiplication – hence \(7 \times 7\) simplifies this repeated addition operation.
• The computed product, which comes from multiplying these two numbers, in our example, results in 49.

Learning multiplication well helps you quickly solve larger mathematical problems and understand more complex concepts in math.

Order of Operations in Calculations

The order of operations is a crucial rule in mathematics that dictates the sequence in which we should perform operations to ensure consistent and accurate results. It helps organize complex expressions and guides us step-by-step through calculations.

A useful acronym to remember this sequence is PEMDAS, which stands for:

• Parentheses - Do these operations first.
• Exponents - Handle all powers or square/square root operations next.
• Multiplication and Division - Resolve these from left to right.
• Addition and Subtraction - Finally, process these operations from left to right.

In our example of \(7^2\), the exponent is computed before any other operations take place, as per the order of operations rule.

Additionally, understanding and applying the order of operations prevents misinterpretation of expressions, ensuring your solutions are reliably correct.