Questions: Simplify. y^3 * y^5 * y * y^2

Simplify. y^3 * y^5 * y * y^2
Transcript text: Simplify. \[ y^{3} \cdot y^{5} \cdot y \cdot y^{2} \]
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Solution

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Solution Steps

To simplify the expression \( y^3 \cdot y^5 \cdot y \cdot y^2 \), we can use the product rule of exponents. The product rule states that when multiplying like bases, we add the exponents. Therefore, we add the exponents of all the \( y \) terms together.

Step 1: Identify the Exponents

We start with the expression \( y^3 \cdot y^5 \cdot y \cdot y^2 \). The exponents of \( y \) are 3, 5, 1, and 2.

Step 2: Apply the Product Rule of Exponents

According to the product rule of exponents, when multiplying like bases, we add the exponents. Therefore, we sum the exponents: \[ 3 + 5 + 1 + 2 = 11 \]

Final Answer

The simplified expression is: \[ \boxed{y^{11}} \]

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