Questions: Simplify the expression. y^3 y^2 y^4 y^10 y^12 y^9

Transcript text: Simplify the expression. \[ y^{3} y^{2} y^{4} \] $y^{10}$ $y^{12}$ $y^{9}$

Solution

Step 1: Identify the exponents

The expression is $ y^{3} y^{2} y^{4} $. Each term has the same base $ y $, but different exponents: 3, 2, and 4.

Step 2: Apply the rule of exponents for multiplication

When multiplying terms with the same base, add the exponents. So, $ y^{3} y^{2} y^{4} = y^{3 + 2 + 4} $.

Step 3: Calculate the sum of the exponents

Add the exponents: $ 3 + 2 + 4 = 9 $. Therefore, $ y^{3} y^{2} y^{4} = y^{9} $.

Step 4: Match the result with the given options

The simplified expression is $ y^{9} $, which matches the third option.

$\boxed{y^{9}}$

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