Which of the following expressions is equivalent to ^3√216/27^1/3 when applying the exponent properties?(1 point)

Question

Responses

1/2
Start Fraction 1 over 2 End Fraction
18
18
2
2
8

Answer 1

To simplify the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\), we can use exponent properties.

First, let's simplify the components:

1. Calculate \(\sqrt[3]{216}\): \[ 216 = 6^3 \Rightarrow \sqrt[3]{216} = 6 \]

2. Calculate \(27^{\frac{1}{3}}\): \[ 27 = 3^3 \Rightarrow 27^{\frac{1}{3}} = 3 \]

Now, substitute these results back into the expression: \[ \frac{\sqrt[3]{216}}{27^{\frac{1}{3}}} = \frac{6}{3} = 2 \]

Thus, the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\) simplifies to \(2\).

The correct response is: \[ \text{2} \]