10. When applying the exponent properties, what is the simplified form of the expression 216√3/27*1/3

Question

?(2 points)
The simplified form of the expression is:

Answer 1

To simplify the expression \( \frac{216\sqrt{3}}{27} \cdot \frac{1}{3} \), let's break it down step by step.

1. Simplify the fraction \( \frac{216}{27} \): \[ 216 \div 27 = 8 \] So, \( \frac{216}{27} = 8 \).

2. Combine the simplified result with \( \sqrt{3} \) and \( \frac{1}{3} \): \[ 8\sqrt{3} \cdot \frac{1}{3} \]

3. Multiply \( 8 \) by \( \frac{1}{3} \): \[ 8 \cdot \frac{1}{3} = \frac{8}{3} \]

4. Thus, the expression becomes: \[ \frac{8\sqrt{3}}{3} \]

Therefore, the simplified form of the expression \( \frac{216\sqrt{3}}{27} \cdot \frac{1}{3} \) is: \[ \frac{8\sqrt{3}}{3} \]