Solve (2×7×3)^(-6): Negative Exponent Expression

To solve this problem, we'll simplify $\left(2\times7\times3\right)^{-6}$ using exponent rules:

• Step 1: Apply the power of a product rule
  The expression is $(2 \times 7 \times 3)^{-6}$. By the power-of-a-product rule, we have: $(2 \times 7 \times 3)^{-6} = 2^{-6} \times 7^{-6} \times 3^{-6}$.
• Step 2: Convert using negative exponent rule
  Use $a^{-n} = \frac{1}{a^n}$, so: $2^{-6} \times 7^{-6} \times 3^{-6} = \frac{1}{2^6 \times 7^6 \times 3^6}$.

Comparing with the given choices:

• Choice 1 suggests $\frac{1}{2^{-6} \times 7^{-6} \times 3^{-6}}$ which is incorrect.
• Choice 2 is $\frac{1}{2^6 \times 7^6 \times 3^6}$, which matches our simplified expression.
• Choice 3 is $\frac{1}{\left(2\times7\times3\right)^6}$ which also matches because: $\frac{1}{(2 \times 7 \times 3)^6} = \frac{1}{2^6 \times 7^6 \times 3^6}$

Since both choices B and C match the simplified expression, we conclude that choice D (B+C are correct) is the correct answer.

Therefore, the correct answer to the problem, as per our solution, is "B+C are correct".