Question

^3√216/27^1/3=
(leave the answer in exponent form)

Answer 1

To solve the expression \(\frac{\sqrt[3]{216}}{27^{1/3}}\), we'll simplify each part.

1. **Simplify \(\sqrt[3]{216}\):**
\[
216 = 6^3 \quad \text{(since } 6 \times 6 \times 6 = 216\text{)}
\]
Therefore,
\[
\sqrt[3]{216} = \sqrt[3]{6^3} = 6.
\]

2. **Simplify \(27^{1/3}\):**
\[
27 = 3^3.
\]
Therefore,
\[
27^{1/3} = (3^3)^{1/3} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3.
\]

3. **Combine the results:**
Now we can substitute these values back into the original expression:
\[
\frac{\sqrt[3]{216}}{27^{1/3}} = \frac{6}{3}.
\]

4. **Simplify the fraction:**
\[
\frac{6}{3} = 2.
\]
To express this in exponent form, we can write:
\[
2 = 2^1.
\]

Thus, the final answer in exponent form is:
\[
\boxed{2^1}.
\]