Question
15. Which expressions are equal to 27 ? Choose all that A. \( 3^{3} \) B. \( 3^{4} \div 3 \) C. \( 3^{3} \cdot \frac{1}{3} \) D. \( 3 \cdot 3 \cdot 3 \) E. \( 3+3+3 \) F. \( 3 \cdot 9 \) G. \( 3^{2} \cdot 3 \) H. \( 3^{9} \)
Ask by Bernard Mejia. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expressions equal to 27 are A, B, D, F, and G.
Solution
To determine which expressions are equal to 27, let's evaluate each option:
**A. \( 3^{3} \)**
\[
3^3 = 3 \times 3 \times 3 = 27
\]
**Correct**
**B. \( 3^{4} \div 3 \)**
\[
3^4 = 81 \\
81 \div 3 = 27
\]
**Correct**
**C. \( 3^{3} \cdot \frac{1}{3} \)**
\[
3^3 = 27 \\
27 \times \frac{1}{3} = 9
\]
**Incorrect**
**D. \( 3 \cdot 3 \cdot 3 \)**
\[
3 \times 3 \times 3 = 27
\]
**Correct**
**E. \( 3 + 3 + 3 \)**
\[
3 + 3 + 3 = 9
\]
**Incorrect**
**F. \( 3 \cdot 9 \)**
\[
3 \times 9 = 27
\]
**Correct**
**G. \( 3^{2} \cdot 3 \)**
\[
3^2 = 9 \\
9 \times 3 = 27
\]
**Correct**
**H. \( 3^{9} \)**
\[
3^9 = 19,\!683
\]
**Incorrect**
**Therefore, the expressions equal to 27 are:**
**A, B, D, F, and G**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Did you know that 27 can be expressed in various ways due to its factors? In fact, it is \(3^3\), which means multiplying 3 by itself three times, resulting in 27! So, options A ( \(3^{3}\) ), B ( \(3^{4} \div 3\) ), D ( \(3 \cdot 3 \cdot 3\) ), F ( \(3 \cdot 9\) ), and G ( \(3^{2} \cdot 3\) ) are equal to 27, while the others certainly do not make the cut! If you want to easily spot which expressions equal 27, it helps to remember that exponential expressions and multiplication are your best friends. Check for factors of 3 and see if they combine correctly to form 27. Avoid common pitfalls like adding 3s together as in option E, which only sums up to 9, far from the target!
