(Laws of Exponents with Integer Exponents LC) Simplify $$ \left(2^{4} ight)^{-1} $$ $$ \begin{array}{l}-2^{4} \ \frac{1}{2^{3}} \ \frac{1}{2^{4}}\end{array} $$

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(Laws of Exponents with Integer Exponents LC) Simplify $$ \left(2^{4}ight)^{-1} $$ $$ \begin{array}{l}-2^{4} \ \frac{1}{2^{3}} \ \frac{1}{2^{4}}\end{array} $$

UpStudy AI · Accepted Answer

To simplify $$ \left(2^{4}\right)^{-1} $$, you can apply the **Laws of Exponents**, specifically the rule:

$$
\left(a^{b}\right)^{c} = a^{b \times c}
$$

**Step-by-Step Solution:**

1. **Apply the Exponent Rule:**
   $$
   \left(2^{4}\right)^{-1} = 2^{4 \times (-1)} = 2^{-4}
   $$

2. **Simplify the Negative Exponent:**
   A negative exponent indicates the reciprocal of the base raised to the positive exponent.
   $$
   2^{-4} = \frac{1}{2^{4}}
   $$

3. **Final Simplified Form:**
   $$
   \frac{1}{2^{4}}
   $$

**Conclusion:**

The simplified form of $$ \left(2^{4}\right)^{-1} $$ is:

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

This corresponds to the third option in your list:

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

(Laws of Exponents with Integer Exponents LC) Simplify \( \left(2^{4}\right)^{-1} \) \( \begin{array}{l}-2^{4} \\ \frac{1}{2^{3}} \\ \frac{1}{2^{4}}\end{array} \)

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