Problem 30 Simplify. See Examples 1 through... [FREE SOLUTION]

Chapter 2: Problem 30

Simplify. See Examples 1 through $10$. $$ |-3+7| \cdot 7^{2} $$

Short Answer

Expert verified

The expression simplifies to 196.

Step by step solution

Simplify the Absolute Value

The expression inside the absolute value is $-3 + 7$. Calculate this to get $-3 + 7 = 4$. Since the absolute value function outputs the non-negative value of its input, $|4| = 4$. Replace $-3 + 7$ with 4 in the expression.

Calculate the Power

Next, calculate $7^2$. This means you multiply 7 by itself: $(7 \times 7) = 49$.

Multiply the Results

Now multiply the results of the previous steps: $4 imes 49$. First, calculate $4 imes 49$. Break this down: $4 imes 49 = 4 \times (50 - 1) = (4 \times 50) - (4 \times 1) = 200 - 4 = 196$.

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Key Concepts

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

Absolute Value

The absolute value of a number expresses its distance from zero on a number line, ignoring its sign.
It is denoted by the vertical lines surrounding the number or expression, such as $|-3+7|$.

Absolute value only results in non-negative numbers.
If the value inside the absolute value symbol is negative, like -3, ignore the sign and consider it a positive number.
For positive numbers or zero, the absolute value remains the same as the original value.

In our example, $-3+7$ first simplifies to $+4$.
The absolute value of $+4$ is simply four, since $|4| = 4$.
Thus, the expression becomes $|-3+7| = 4$. Remember, absolute value eliminates any negativity!

Exponentiation

Exponentiation involves raising a number to a certain power, indicating how many times to multiply it by itself.
It is written with a base and an exponent, such as $7^2$ in this problem.

The base is the number that you multiply, which, in our case, is 7.
The exponent (or power) is the tiny number placed at the top right of the base, 2 in this instance, telling us to multiply 7 by itself once.

So, $7^2$ means $7 \times 7$.
Performing this multiplication results in 49.
Exponentiation allows for rapid computation and understanding of repeated multiplication.

Multiplication Steps

Multiplication is the process of scaling one number by another.
It is a fundamental operation in arithmetic where we take a series of product steps to come to a final result.

Start with the numbers you need to multiply, $4$ and $49$ here.
Use distributive property if necessary to simplify, such as breaking down large numbers.
For $4 \times 49$, think of 49 as $50 - 1$ to make calculation easier.

This method involves calculating $4 \times 50 = 200$ and $4 \times 1 = 4$,
then subtracting: $200 - 4 = 196$.
Decomposing numbers in multiplication helps manage and solve more complex problems efficiently.
Practice and familiarity can enhance speed and proficiency in multiplication.

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91影视

Simplify. See Examples 1 through \(10\). $$ |-3+7| \cdot 7^{2} $$

Short Answer

Step by step solution

Simplify the Absolute Value

Calculate the Power

Multiply the Results

Key Concepts

Absolute Value

Exponentiation

Multiplication Steps

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