use the properties of exponents to perform the following operation:
2^1/3 *8^¼
2^13/12
2^2/7
2^¼
16^1/12
16^2/7
To perform the operation 2^(1/3) * 8^(1/4), we can use the property that (a^m) * (a^n) = a^(m+n).
First, let's simplify 2^(1/3) = 2^(1/3).
Then, let's simplify 8^(1/4) = (2^3)^(1/4) = 2^(3/4).
Now we can apply the property mentioned earlier to get:
2^(1/3) * 8^(1/4) = 2^(1/3 + 3/4).
To combine the fractions, we need a common denominator of 12.
1/3 = 4/12 and 3/4 = 9/12.
Therefore, 2^(1/3 + 3/4) = 2^(4/12 + 9/12) = 2^(13/12).
Therefore, the answer is 2^(13/12).