Given that the cube root of 27 is 3, what is 27^4/3

Answer 1

To find \( 27^{4/3} \), we can simplify it step by step.

1. We know that \( 27 = 3^3 \).
2. Therefore, we can rewrite \( 27^{4/3} \) as: \[ (3^3)^{4/3} \]
3. Applying the power of a power property \((a^m)^n = a^{m \cdot n}\), we get: \[ 3^{3 \cdot (4/3)} = 3^4 \]
4. Now, we need to calculate \( 3^4 \): \[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

Thus, \( 27^{4/3} = 81 \).