Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 3^{-3} = \frac{1}{27} \)
Solution
To evaluate \( 3^{-3} \), we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \) for any non-zero number \( a \) and positive integer \( n \).
\[
3^{-3} = \frac{1}{3^3}
\]
Now, calculate \( 3^3 \):
\[
3^3 = 3 \times 3 \times 3 = 27
\]
Therefore,
\[
3^{-3} = \frac{1}{27}
\]
**Final Answer:**
\( 3^{-3} = \dfrac{1}{27} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Did you know that negative exponents are like a secret code for division? For \( 3^{-3} \), it's equivalent to \( \frac{1}{3^3} \). So, instead of worrying about negatives, just think of it as the inverse of cubing 3! Multiply 3 by itself three times, and you get 27. Thus, \( 3^{-3} = \frac{1}{27} \). When dealing with negative exponents, a common mistake is forgetting that they imply reciprocals. Always remember to switch the base to the denominator for negative exponents! If you find yourself unsure, try rewriting the expression step by step, like unwrapping a present to see what’s inside!
