Given that the cube root of 27 is 3, what is 2743

Question

?(1 point)
Responses

108
108

4
4

81
81

12

Answer 1

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

1. First, we can express \( 27 \) as \( 3^3 \).
2. Then, 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 get:

\[ 3^{3 \cdot (4/3)} = 3^4 \]

4. Now, calculate \( 3^4 \):

\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

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

The correct response is 81.