Use the Power Rule of Exponents to create a simplified equivalent expression of

Question

(12 x 12 x 12) x (12 x 12 x 12).

Answer 1

To simplify the expression \((12 \times 12 \times 12) \times (12 \times 12 \times 12)\) using the Power Rule of Exponents, we first recognize that each set of three 12s can be written in exponential form.

Each group of three 12s can be expressed as: \[ 12 \times 12 \times 12 = 12^3. \]

Therefore, we can rewrite the original expression as: \[ (12^3) \times (12^3). \]

Using the Power Rule of Exponents, which states that \(a^m \times a^n = a^{m+n}\), we can combine the two terms: \[ 12^3 \times 12^3 = 12^{3+3} = 12^6. \]

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