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

Question

?(1 point)
Responses

4
4

81
81

12
12

108

Answer 1

To solve \( 27^{4/3} \), we can break it down as follows:

1. First, we know that the cube root of 27 is 3, so we can express 27 as \( 27 = 3^3 \).
2. Thus, we can rewrite \( 27^{4/3} \) as \( (3^3)^{4/3} \).
3. Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we have: \[ (3^3)^{4/3} = 3^{3 \cdot (4/3)} = 3^4 \]
4. Now, we can calculate \( 3^4 \): \[ 3^4 = 81 \]

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

The correct response is 81.