https://r2.erweima.ai/mathbot/image/172563730702896oec9ah.jpg

can you explain to me how to get from the first example to the second one

In the image, it looks like we are simplifying an expression that involves a product of terms. Let's break down the transformation step by step:

### Step 1: Starting Expression
From the first line of the image, we see the expression:

\[
x^2 \cdot \left(\frac{2}{2}\right) \cdot 2
\]

### Step 2: Simplification of the Fraction \(\frac{2}{2}\)
Notice that \(\frac{2}{2}\) simplifies to 1 because:

\[
\frac{2}{2} = 1
\]

Thus, the expression becomes:

\[
x^2 \cdot 1 \cdot 2
\]

Since multiplying by 1 does not change the value of the expression, we are left with:

\[
x^2 \cdot 2
\]

### Step 3: Rewriting the Expression
In the second equation, we see a slightly rearranged version of the same expression. It is written as:

\[
\left(\frac{x^2}{2}\right) \cdot (2 \cdot 2)
\]

This step involves a reorganization of the terms. What happened here is that the term \(2\) from the original expression was factored and grouped as follows:

\[
x^2 \cdot 2 = \left(\frac{x^2}{2}\right) \cdot (2 \cdot 2)
\]

This transformation is valid because multiplying both the numerator and denominator by the same factor does not change the overall value.

### Conclusion
The move from the first to the second expression involves two main steps:
1. Simplifying \(\frac{2}{2}\) to 1.
2. Rearranging and factoring the expression by distributing \(2\) appropriately.

Would you like further clarification or details about specific parts of this transformation?

Here are some related questions to deepen understanding:
1. Why is \(\frac{2}{2}\) simplified to 1, and does this affect the overall equation?
2. How does factoring \(x^2 \cdot 2\) into \(\frac{x^2}{2} \cdot 2 \cdot 2\) help with solving or simplifying the equation?
3. What other properties of exponents and multiplication are used in this simplification process?
4. Could you explain how distribution works in expressions like this, especially when dealing with powers and fractions?
5. How would this simplification process differ if the exponent was not 2 but another number?

Tip: When simplifying algebraic expressions, always look for common factors that can be distributed or factored out for easier manipulation.

Can you explain how to get from the first example to the second one?

Learn how to simplify algebraic expressions involving exponents and fractions step by step. This problem illustrates key algebraic concepts like simplification, factoring, and properties of exponents. Suitable for high school students.

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