Question
use the power rule of exponent to simplify the expression (12 x 12 x 12)x( 12 x 12 x 12)
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Answered by
GPT-4o mini
To simplify the expression \((12 \times 12 \times 12) \times (12 \times 12 \times 12)\), we can first express each group of \(12\)s using exponents.
Each group \( (12 \times 12 \times 12) \) contains three \(12\)s, which can be written as:
\[
12^3
\]
Thus, the entire expression can be rewritten as:
\[
(12^3) \times (12^3)
\]
Using the power rule of exponents, which states that \(a^m \times a^n = a^{m+n}\), we combine the exponents:
\[
12^3 \times 12^3 = 12^{3+3} = 12^6
\]
Therefore, the simplified expression is:
\[
12^6
\]
Each group \( (12 \times 12 \times 12) \) contains three \(12\)s, which can be written as:
\[
12^3
\]
Thus, the entire expression can be rewritten as:
\[
(12^3) \times (12^3)
\]
Using the power rule of exponents, which states that \(a^m \times a^n = a^{m+n}\), we combine the exponents:
\[
12^3 \times 12^3 = 12^{3+3} = 12^6
\]
Therefore, the simplified expression is:
\[
12^6
\]
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