Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 216^{\frac{2}{3}} = 36 \)
Solution
To evaluate \( 216^{\frac{2}{3}} \), follow these steps:
1. **Express 216 as a Power of 6:**
\[
216 = 6^3
\]
2. **Apply the Exponent Rule \((a^b)^c = a^{b \cdot c}\):**
\[
216^{\frac{2}{3}} = (6^3)^{\frac{2}{3}} = 6^{3 \cdot \frac{2}{3}} = 6^2
\]
3. **Calculate \(6^2\):**
\[
6^2 = 36
\]
**Final Answer:**
\( 216^{\frac{2}{3}} = 36 \)
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Explain 
Simplify this solution Mind Expander
To evaluate \( 216^{\frac{2}{3}} \), we start by rewriting the expression using the property of exponents. The expression can be split into two parts: \[ 216^{\frac{2}{3}} = \left(216^{\frac{1}{3}}\right)^2 \] Next, we need to find \( 216^{\frac{1}{3}} \), which is the cube root of 216. Since \( 216 = 6^3 \), we can determine: \[ 216^{\frac{1}{3}} = 6 \] Now, we can square the result: \[ \left(216^{\frac{1}{3}}\right)^2 = 6^2 = 36 \] Thus, the final value of \( 216^{\frac{2}{3}} \) is: \[ \boxed{36} \]
