5. If $$ x^{-3}=27, x= $$ (A) -3 (B) $$ -\frac{1}{3} $$ (C) $$ \frac{1}{3} $$ (D) 3 (E) 9

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To solve the equation $$ x^{-3} = 27 $$, we can follow these steps:

1. **Rewrite the equation**: The expression $$ x^{-3} $$ can be rewritten as $$ \frac{1}{x^3} $$. Therefore, we have:
   $$
   \frac{1}{x^3} = 27
   $$

2. **Cross-multiply**: To eliminate the fraction, we can cross-multiply:
   $$
   1 = 27x^3
   $$

3. **Isolate $$ x^3 $$**: Now, we can solve for $$ x^3 $$ by dividing both sides by 27:
   $$
   x^3 = \frac{1}{27}
   $$

4. **Take the cube root**: To find $$ x $$, we take the cube root of both sides:
   $$
   x = \sqrt[3]{\frac{1}{27}}
   $$

5. **Calculate the cube root**: The cube root of $$ \frac{1}{27} $$ is $$ \frac{1}{3} $$ because $$ \left(\frac{1}{3}\right)^3 = \frac{1}{27} $$.

Thus, the solution is:
$$
x = \frac{1}{3}
$$

The correct answer is (C) $$ \frac{1}{3} $$.
$$ x = \frac{1}{3} $$, choice C.

5. If \( x^{-3}=27, x= \) (A) -3 (B) \( -\frac{1}{3} \) (C) \( \frac{1}{3} \) (D) 3 (E) 9

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