# How do you simplify 12^-4/2^-4?

Nov 27, 2016

$\frac{1}{{2}^{4} \cdot {3}^{4}}$

#### Explanation:

Write 12 as the product of its prime factors, in that way there will be a power of 2 which can be simplified.

Recall a law of indices dealing with negative indices.

${x}^{-} m = \frac{1}{x} ^ m \text{ and } \frac{1}{x} ^ - m = {x}^{m}$

${12}^{-} \frac{4}{2} ^ - 4 = {2}^{4} / {12}^{4}$

=${2}^{4} / {\left({2}^{2} \times 3\right)}^{4}$

=${2}^{4} / \left({2}^{8} \cdot {3}^{4}\right)$

=$\frac{1}{{2}^{4} \cdot {3}^{4}} \text{ } \leftarrow$ subtract the indices of like bases