Question

27^2/3 in radical form

Answer 1

To express \( 27^{2/3} \) in radical form, we start by breaking it down:

1. Rewrite \( 27 \) as a power of a base. We know that:
\[
27 = 3^3
\]

2. Substitute \( 27 \) with \( 3^3 \):
\[
27^{2/3} = (3^3)^{2/3}
\]

3. Use the property of exponents \((a^m)^n = a^{m \cdot n}\):
\[
(3^3)^{2/3} = 3^{3 \cdot (2/3)} = 3^2
\]

4. Calculate \( 3^2 \):
\[
3^2 = 9
\]

To put this in radical form:
- The exponent \(\frac{2}{3}\) can be represented as a radical:
\[
27^{2/3} = \sqrt[3]{27^2}
\]

Calculating \( 27^2 \):
\[
27^2 = 729
\]
Thus,
\[
\sqrt[3]{27^2} = \sqrt[3]{729}
\]

Therefore, \( 27^{2/3} \) in radical form is:
\[
\sqrt[3]{729}
\]

In conclusion, \( 27^{2/3} \) can be expressed as \( 9 \) or in radical form as \( \sqrt[3]{729} \).