use the properties of exponents to perform the following operation
2^1/3 * 8^1/4
A)2^1/3
B)2^13/12
C)16^2/7
D)2^2/7
E)16^1/12
To perform the operation 2^(1/3) * 8^(1/4), we can simplify each base separately.
First, let's simplify 2^(1/3):
We know that the cube root of 2 is equal to 2^(1/3), so we can rewrite 2^(1/3) as the cube root of 2.
Next, let's simplify 8^(1/4):
We know that the fourth root of 8 is equal to 2, so we can rewrite 8^(1/4) as the fourth root of 8, which is 2.
Now we can rewrite the original expression as the product of the simplified bases:
2^(1/3) * 8^(1/4) = (cube root of 2) * (fourth root of 8)
Using the property of exponents (a * b)^n = a^n * b^n, we can simplify this expression further:
(cube root of 2) * (fourth root of 8) = (2^(1/3))^3 * (2^(1/4))^4 = 2^(3*1/3) * 2^(4*1/4)
= 2^1 * 2^1
= 2^2
Therefore, the simplified expression is 2^2, which is equal to 4.
The correct answer is:
D) 2^2/7