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Answer 1

To simplify the expression \( 2(k^{-4}) - 3(2k^{-1}) \), we first rewrite the terms:

1. The first term \( 2(k^{-4}) \) is equivalent to \( \frac{2}{k^4} \).
2. The second term \( 3(2k^{-1}) \) can be simplified to \( 6(k^{-1}) = \frac{6}{k} \).

Thus we have:

\[ \frac{2}{k^4} - \frac{6}{k} \]

To perform the subtraction, we need a common denominator. The least common denominator (LCD) of \( k^4 \) and \( k \) is \( k^4 \). We rewrite \( \frac{6}{k} \) to have the denominator \( k^4 \):

\[ \frac{6}{k} = \frac{6k^3}{k^4} \]

Now, the expression becomes:

\[ \frac{2}{k^4} - \frac{6k^3}{k^4} = \frac{2 - 6k^3}{k^4} \]

Thus, the result of the subtraction is:

\[ \frac{2 - 6k^3}{k^4} \]

This cannot be simplified further. Therefore, the result is:

\[ \frac{2 - 6k^3}{k^4} \]