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

Question

?(1 point)
Responses

4
4

108
108

12
12

81
81

Answer 1

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

1. Recognize that \( 27 = 3^3 \).
2. Then, \( 27^{4/3} = (3^3)^{4/3} \).

Using the property of exponents \((a^m)^n = a^{m \cdot n}\):

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

Now calculate \( 3^4 \):

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

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

The correct response is: