Use the properties of exponents to perform the following operation:

Question

2^1/3 * 8^1/4

Answer Choices:

2^13/12

2^2/7

16^1/12

16^2/7

2^1/4

Answer 1

We can simplify each exponent before multiplying.

First, let's simplify the exponent 1/3:
2^(1/3) can be written as the cube root of 2.

Next, let's simplify the exponent 1/4:
8^(1/4) can be written as the fourth root of 8.

The cube root of 2 is equal to 2^(1/3) = 2^(4/12).
The fourth root of 8 is equal to 8^(1/4) = 2^(3/4).

Now we can rewrite the expression with the simplified exponents:
2^(4/12) * 2^(3/4).

When multiplying terms with the same base, we add the exponents:
2^(4/12 + 3/4).

To add the fractions, we need a common denominator of 12:
4/12 + 3/4 = (4/12) * (1/1) + (3/4) * (3/3) = 4/12 + 9/12 = 13/12.

Therefore, the final answer is 2^(13/12), which is not one of the given answer choices.