https://r2.erweima.ai/mathbot/image/1726309387283ke55n36w.jpg

The image you provided is asking which expression of \( 3^{3^3} \) is correct. There are two approaches shown, and we need to determine which one is valid based on the order of operations.

### Left Side:

\[
3^{3^3} = (3^3)^3
\]

1. Compute \( 3^3 = 27 \).
2. Then \( 27^3 = 19683 \).

### Right Side:

\[
3^{3^3} = 3^{(3^3)}
\]

1. First, compute \( 3^3 = 27 \).
2. Then, \( 3^{27} = 7625597484987 \).

### Conclusion:
The correct answer follows the right side approach because the expression \( 3^{3^3} \) means you should calculate the exponent first. This gives you \( 3^{27} \), which equals **7,625,597,484,987**.

The left side's interpretation of \( (3^3)^3 \), which equals **19,683**, is incorrect. Therefore, the **right side is correct**.

Would you like more details or have further questions?

Here are 5 related questions to deepen understanding:
1. How do the rules of order of operations apply to exponential expressions?
2. What is the difference between \( (a^b)^c \) and \( a^{b^c} \)?
3. How do you compute powers with large exponents efficiently?
4. Can \( 3^{27} \) be simplified further using logarithms?
5. What other mathematical rules are frequently misunderstood like this one?

**Tip:** When dealing with multiple exponents, always resolve them from top to bottom, i.e., compute the highest exponent first.

Which interpretation of 3^3^3 is correct: (3^3)^3 or 3^(3^3)?

Learn how to properly interpret the expression 3^3^3 by understanding the order of operations in exponential terms. This problem demonstrates the difference between (3^3)^3 and 3^(3^3), showing the correct solution is 7,625,597,484,987. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation