Solve (1/24)^(-2): Negative Exponent with Product Denominator

Insert the corresponding expression:

$\left(\frac{1}{2\times3\times4}\right)^{-2}=$

We are given the expression: $\left(\frac{1}{2\times3\times4}\right)^{-2}$. We need to simplify it using the rules of exponents.

• Step 1: Identify the base of the exponent.
  The base is $\frac{1}{2\times3\times4}$.
  

• Step 2: Apply the rule for negative exponents.
  For a fraction $\frac{1}{a}$ with a negative exponent, $\left( \frac{1}{a} \right)^{-n} = a^n$. Therefore, $\left(\frac{1}{2\times3\times4}\right)^{-2} = (2\times3\times4)^2$.
  

• Step 3: Expand the expression.
  $(2\times3\times4)^2 = 2^2 \times 3^2 \times 4^2$.

Thus, the simplified expression is: $2^2\times3^2\times4^2$