Problem 26 Simplify. $$ 2^{2}+5^{2} $... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 26

Simplify. $$ 2^{2}+5^{2} $$

Short Answer

Expert verified

Step by step solution

- Evaluate the powers

First, calculate the values of the individual powers. For $2^2$, multiply 2 by itself: \[ 2^2 = 2 \times 2 = 4 \] For $5^2$, multiply 5 by itself: \[ 5^2 = 5 \times 5 = 25 \]

- Add the results

Now, add the values that were found in Step 1. \[ 4 + 25 \]

- Simplify the addition

Simplify the addition from Step 2 by performing the arithmetic operation: \[ 4 + 25 = 29 \]

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Key Concepts

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

exponents

Understanding exponents is crucial in simplifying expressions. An exponent indicates how many times a number, known as the base, is multiplied by itself. In our example, we have the expressions $2^2$ and $5^2$.

Let's break down what this means:

For $2^2$, the base is 2, and it's raised to the power of 2. This means we multiply 2 by itself: $2^2 = 2 \times 2 = 4$.
For $5^2$, the base is 5, and it's raised to the power of 2. This means we multiply 5 by itself: $5^2 = 5 \times 5 = 25$.

These steps help us convert the exponential expressions into simpler arithmetic values.

addition

Addition is one of the fundamental arithmetic operations. When adding numbers, you combine their values to find the total. In our example, after simplifying the exponents, we need to add $4$ and $25$.

Here is how you can approach it:

First, write down the numbers you want to add: $4$ and $25$.
Next, perform the addition: $4 + 25$.
Finally, find the sum, which in this case is $29$.

Addition works the same way regardless of the numbers involved. Learning to add correctly ensures accuracy in mathematical problems.

arithmetic operations

Arithmetic operations form the basis of most mathematical calculations. These operations include addition, subtraction, multiplication, and division. In the context of our example, we used both exponents and addition to arrive at the solution.

Here's how to approach arithmetic operations:

First, identify the operations you need to perform (in our case, exponents and addition).
Next, follow the order of operations (commonly known as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Finally, simplify each step carefully to avoid errors.

By mastering arithmetic operations, you can simplify complex expressions and solve mathematical problems efficiently.

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91影视

Simplify. $$ 2^{2}+5^{2} $$

Short Answer

Step by step solution

- Evaluate the powers

- Add the results

- Simplify the addition

Key Concepts

exponents

addition

arithmetic operations

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