Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12)

Question

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Answer 1

Using the Power Rule of Exponents, we know that \(a^m \cdot a^n = a^{m+n}\).

First, let's rewrite the expression \((12 \cdot 12 \cdot 12) \cdot (12 \cdot 12 \cdot 12)\):

1. Each group of \(12 \cdot 12 \cdot 12\) can be rewritten using exponents: \[ 12 \cdot 12 \cdot 12 = 12^3 \] So the expression becomes: \[ (12^3) \cdot (12^3) \]

2. Now, applying the Power Rule: \[ (12^3) \cdot (12^3) = 12^{3+3} = 12^6 \]

Therefore, the simplified equivalent expression is: \[ \boxed{12^6} \]