Which of the following are equivalent to the expression x 1/3 times x 1/2? Select all the correct answers that apply and show your work.
a) x 1/2 times 1/3
b) x 1/2 + 1/3
c) 6 square root of f x^5
d) x 1/6
The expression x 1/3 times x 1/2 can be simplified by using the rule for multiplying exponents:
x^(1/3) * x^(1/2) = x^(1/3 + 1/2) = x^(5/6)
Therefore, the equivalent expressions are:
c) 6 square root of f x^5
d) x^(1/6)
The answers you gave D) x 1/6 should be B) x 1/2 + 1/3 C) 6 square root of x^5 is correct. Please Show your work for B and C
Apologies for the mistake. Let's go through the correct calculations for options B and C:
B) To find the equivalent expression for x 1/3 times x 1/2, we can multiply the fractions:
x^(1/3) * x^(1/2) = x^(1/3 + 1/2) = x^(2/6 + 3/6) = x^(5/6)
Therefore, the expression x 1/3 times x 1/2 is equivalent to x^(5/6), which is represented as x 1/2 + 1/3.
C) To find the equivalent expression for x 1/3 times x 1/2, we can also flip the exponents and multiply:
x^(1/3) * x^(1/2) = x^(1/3) * x^(2/2) = x^(1/3) * x = x^(1/3 + 1) = x^(4/3)
Therefore, the expression x 1/3 times x 1/2 is equivalent to x^(4/3), which is represented as 6 square root of x^5.
I think you mean:
which is represented as x^(1/2 + 1/3)
Apologies for the confusion in my previous response. You are correct:
To find the equivalent expression for x^(1/3) times x^(1/2), we can add the exponents:
x^(1/3) * x^(1/2) = x^(1/3 + 1/2) = x^(2/6 + 3/6) = x^(5/6)
Therefore, the expression x^(1/3) times x^(1/2) is equivalent to x^(5/6), which is represented as x^(1/2 + 1/3).
So, the correct options are B) x^(1/2 + 1/3) and C) 6 square root of x^5.
C) 6 square root of x^5.
is
6 x^(5/2)
maybe you mean
(x^5)^(1/6)
Apologies for the confusion. You are correct.
To clarify, the equivalent expression for x^(1/3) times x^(1/2) is x^(5/6).
C) 6 square root of x^5 can be simplified as 6 times the square root of x^5, which is 6 * x^(5/2).
So the correct options are B) x^(1/2 + 1/3) and C) 6 * x^(5/2) or alternatively, (x^5)^(1/6).
How do you get 6 * x^(5/2) ?????
I apologize for the incorrect response. Let's correct the explanation:
To find the equivalent expression for x^(1/3) times x^(1/2), we can add the exponents:
x^(1/3) * x^(1/2) = x^(1/3 + 1/2) = x^(2/6 + 3/6) = x^(5/6).
Therefore, the expression x^(1/3) times x^(1/2) is equivalent to x^(5/6), not 6 * x^(5/2) as previously stated.
So, the correct options are B) x^(1/2 + 1/3) and C) (x^5)^(1/6).