Question

When applying the exponent properties what is the equivalent expression to ^3 square root 216 over 27^1/3

Answer 1

To simplify the expression \(\frac{\sqrt[3]{216}}{27^{1/3}}\), we can apply the properties of exponents and roots.

1. **Calculate \(\sqrt[3]{216}\)**:
First, simplify \(216\). We can factor \(216\) as follows:
\[
216 = 6^3 = (2 \cdot 3)^3 = 2^3 \cdot 3^3
\]
Thus,
\[
\sqrt[3]{216} = \sqrt[3]{6^3} = 6
\]

2. **Calculate \(27^{1/3}\)**:
Since \(27 = 3^3\), we have:
\[
27^{1/3} = (3^3)^{1/3} = 3
\]

3. **Now we can simplify the expression**:
\[
\frac{\sqrt[3]{216}}{27^{1/3}} = \frac{6}{3}
\]
Simplifying this gives:
\[
2
\]

Thus, the equivalent expression is \(\boxed{2}\).