Rational Exponents Quick Check

Question

2 of 52 of 5 Items
Question
Given that the cube root of 27 is 3, what is 2743
?(1 point)
Responses

108
108

81
81

4
4

12

Answer 1

To evaluate \(27^{\frac{4}{3}}\), we can break it down into two parts:

1. First, find the cube root of 27, which is \(3\).
2. Then, raise that result to the 4th power.

So let's calculate it:

\[ 27^{\frac{4}{3}} = (27^{\frac{1}{3}})^4 = 3^4 = 81 \]

Thus, the answer is \(81\).