Simplify 1/(4^-6 × 7^-6): Negative Exponents in Denominators

To solve this problem, we will simplify the given expression $\frac{1}{4^{-6}\times7^{-6}}$ by using the properties of exponents.

First, note that both $4^{-6}$ and $7^{-6}$ can be combined under the power of a product property:

• $4^{-6} \times 7^{-6} = (4 \times 7)^{-6}$

Then, simplify the expression inside the original fraction:

$\frac{1}{(4 \times 7)^{-6}} = (4 \times 7)^6$

We use the principle that the negative sign in the exponent of a denominator can be inverted to a positive sign in the numerator. Hence, the negative exponent in the denominator becomes positive in the numerator.

Therefore, the correctly corresponding expression to $\frac{1}{4^{-6}\times7^{-6}}$ is $(4 \times 7)^6$.