se the properties of exponents to perform the following operation: 2^1/3 x 8^1/4
1 point)
16^1/12
2^2/7
2^1/4
2^13^12
16^2/7
To perform the operation (2^1/3) x (8^1/4), we can first simplify each exponent separately:
2^1/3 can be rewritten as the cube root of 2
8^1/4 can be rewritten as the fourth root of 8
Using the properties of exponents, we can multiply these two expressions together:
(cube root of 2) x (fourth root of 8)
Now, we need to simplify further:
The cube root of 2 can be simplified to 2^(1/3)
The fourth root of 8 can be simplified to 8^(1/4)
So now we have:
2^(1/3) x 8^(1/4)
Next, we can simplify the bases:
2^(1/3) can be rewritten as 2^(4/12)
8^(1/4) can be rewritten as 2^(3/4)
Therefore, the expression simplifies to:
2^(4/12) x 2^(3/4)
Now, we can use the property of exponents that states that when multiplying two numbers with the same base, we add the exponents:
2^(4/12 + 3/4)
Adding the exponents:
2^(16/48 + 36/48)
Simplifying:
2^(52/48)
Now, we can simplify the exponent:
52/48 can be simplified to 13/12
Therefore, the final simplified expression is:
2^(13/12)