Solve (1/5×6×7)^(-3): Negative Exponent with Sequential Products

Insert the corresponding expression:

$\left(\frac{1}{5\times6\times7}\right)^{-3}=$

To solve the expression $\left(\frac{1}{5\times6\times7}\right)^{-3}$, follow these steps:

• Step 1: Recognize that the expression $\left(\frac{1}{5\times6\times7}\right)^{-3}$ has a negative exponent.
• Step 2: Use the rule for negative exponents: $\left(\frac{1}{a}\right)^{-n} = a^{n}$.
• Step 3: Apply the rule: $\left(\frac{1}{5\times6\times7}\right)^{-3} = \left(5\times6\times7\right)^{3}$.

Therefore, the expression simplifies to $\left(5\times6\times7\right)^3$.

The correct answer is $\left(5\times6\times7\right)^3$.