Question

Given that the cube root of 27 is 3, what is 27^4/3
?(1 point)
Responses

A) 81

B) 12

C) 4

D) 108

Answer 1

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

1. We can rewrite \( 27 \) as \( 3^3 \):
\[
27 = 3^3
\]

2. Now substitute \( 27 \) in the expression:
\[
27^{4/3} = (3^3)^{4/3}
\]

3. When raising a power to another power, you multiply the exponents:
\[
(3^3)^{4/3} = 3^{3 \cdot (4/3)} = 3^4
\]

4. Now calculate \( 3^4 \):
\[
3^4 = 81
\]

Therefore, the value of \( 27^{4/3} \) is \( 81 \).

So the correct answer is:

**A) 81**