6. If $$ n^{-4}=\frac{1}{28,561} $$, what could be the value of $$ n $$ ? (A) $$ \frac{1}{169} $$ (B) $$ -\frac{1}{13} $$ (C) $$ \frac{1}{28,561} $$ (D) $$ \frac{1}{13} $$ (E) 13

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UpStudy AI · Accepted Answer

To solve the equation $$ n^{-4} = \frac{1}{28,561} $$, we can follow these steps:

1. **Rewrite the equation**: The expression $$ n^{-4} $$ can be rewritten as $$ \frac{1}{n^4} $$. Therefore, we have:
   $$
   \frac{1}{n^4} = \frac{1}{28,561}
   $$

2. **Cross-multiply**: This gives us:
   $$
   n^4 = 28,561
   $$

3. **Take the fourth root**: To find $$ n $$, we need to take the fourth root of both sides:
   $$
   n = \sqrt[4]{28,561}
   $$

Next, we will calculate $$ \sqrt[4]{28,561} $$ to find the possible values of $$ n $$.

Let's calculate $$ \sqrt[4]{28,561} $$.

First, we can find $$ \sqrt{28,561} $$ and then take the square root of that result.

Calculating $$ \sqrt{28,561} $$:
$$
\sqrt{28,561} = 169
$$

Now, we take the square root of $$ 169 $$:
$$
\sqrt{169} = 13
$$

Thus, we have:
$$
n = \sqrt[4]{28,561} = 13
$$

Now, let's check the options provided:
- (A) $$ \frac{1}{169} $$
- (B) $$ -\frac{1}{13} $$
- (C) $$ \frac{1}{28,561} $$
- (D) $$ \frac{1}{13} $$
- (E) 13

The value of $$ n $$ that we found is $$ 13 $$, which corresponds to option (E).

Therefore, the answer is:
$$
\boxed{13}
$$
$$ n = 13 $$

6. If \( n^{-4}=\frac{1}{28,561} \), what could be the value of \( n \) ? (A) \( \frac{1}{169} \) (B) \( -\frac{1}{13} \) (C) \( \frac{1}{28,561} \) (D) \( \frac{1}{13} \) (E) 13

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