Questions: Simplify. (3^4 cdot 3^2=)

Transcript text: Simplify. $3^{4} \cdot 3^{2}=$

Solution

Step 1: Apply the Law of Exponents for Multiplication

When multiplying powers with the same base, add the exponents. The law states: \[ a^{m} \cdot a^{n} = a^{m+n} \]

Step 2: Substitute the Given Values

Substitute $ a = 3 $, $ m = 4 $, and $ n = 2 $ into the equation: \[ 3^{4} \cdot 3^{2} = 3^{4+2} \]

Step 3: Simplify the Exponents

Add the exponents: \[ 3^{4+2} = 3^{6} \]

$\boxed{3^{6}}$

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