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

Responses

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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:
\[
\text{2}
\]