Problem 43 Simplify. \(4 \cdot 5^{2}\)... [FREE SOLUTION]

Chapter 15: Problem 43

Simplify. \(4 \cdot 5^{2}\)

Short Answer

Expert verified

100.

Step by step solution

Evaluate the Exponent

First, evaluate the exponent in the expression. Calculate the value of the exponent by finding the value of \( 5^2 \). Since \( 5 \times 5 = 25 \), we can replace \( 5^2 \) with 25.

Multiply the Result

Next, multiply the result from the first step with 4. So, \( 4 \times 25 \) needs to be calculated. Compute the multiplication: \( 4 \times 25 = 100 \).

Write the Simplified Result

Finally, write the simplified result. After multiplying, the expression \( 4 \times 5^2 \) simplifies to 100.

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Key Concepts

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

simplification

Simplification is the process of breaking down complex mathematical expressions into simpler forms. This helps in making calculations easier and reduces the chances of error.

For instance, in the exercise given, the expression is simplified from \( 4 \cdot 5^{2} \) to 100. We do this by first figuring out any exponents, and then performing the remaining operations such as multiplication or division.

When you simplify correctly, you make solving the rest of the problem a lot less complicated. Always remember to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

multiplication

Multiplication is a fundamental math operation involving the combination of equal groups. In our problem, once we evaluated \( 5^2 \) to get 25, we needed to multiply this result by 4.

The multiplication step was \( 4 \times 25 \). Here's a simple procedure to verify:

Write down the numbers you want to multiply: 4 and 25
Remember, multiplication can be seen as repeated addition. So, 4 multiplied by 25 means adding 25 four times: 25 + 25 + 25 + 25 = 100.
Using more advanced methods, you can also multiply the units place and tens place values accordingly, still arriving at 100.

Correctly performing multiplication ensures accurate results in your math problems and simplifies the overall solution process.

evaluating exponents

Evaluating exponents is the process of calculating the power of a number. An exponent indicates how many times a number, called the base, is multiplied by itself.

In this case, our base was 5 and the exponent was 2, written as \( 5^2 \). To evaluate this, you multiply 5 by itself, which gives:
\[ 5 \times 5 = 25 \]

Steps to evaluate exponents:

Identify the base and the exponent
Multiply the base by itself as many times as the exponent indicates
Write down the result. In our case, it鈥檚 25

Evaluating exponents correctly is vital in simplifying and solving various mathematical expressions, as it breaks down more complex calculations into straightforward arithmetic.

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91影视

Simplify. \(4 \cdot 5^{2}\)

Short Answer

Step by step solution

Evaluate the Exponent

Multiply the Result

Write the Simplified Result

Key Concepts

simplification

multiplication

evaluating exponents

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