Which of the following are equivalent to the expression x1/3 x x1/2? Choose all that apply.
a) x1/2 x 1/3
b) x1/2 + 1/3
c) x1/6
d) x5/6
e) 6 square root of x
f) 6 square roof of x^5
To solve this problem, we can simplify the expression x^(1/3) * x * x^(1/2) by combining the exponents and multiplying the bases.
First, we combine the exponents by using the rule x^a * x^b = x^(a+b):
x^(1/3) * x * x^(1/2) = x^(1/3 + 1) * x^(1/2) = x^(4/3) * x^(1/2)
Next, we multiply the bases by using the rule x^a * x^b = x^(a+b):
x^(4/3) * x^(1/2) = x^(4/3 + 1/2) = x^(8/6 + 3/6) = x^(11/6)
Therefore, the expression is equivalent to x^(11/6).
Now, let's go through the given options:
a) x^(1/2) * (1/3)
This is not equivalent to the expression.
b) x^(1/2) + 1/3
This is not equivalent to the expression.
c) x^(1/6)
This is not equivalent to the expression.
d) x^(5/6)
This is not equivalent to the expression.
e) 6√x (6 square root of x)
This is equivalent to x^(1/2), which is not equivalent to the expression.
f) 6√x^5 (6 square root of x^5)
This is equivalent to 6 * x^(5/2), which is not equivalent to the expression.
Therefore, none of the given options are equivalent to the expression.