Answer:
D
Step-by-step explanation:
Which of the following is equivalent to (a^1/2 * b^1/3)^1/2?
Note: To distribute exponents in a parentheses where the two variables are being multiplied, you can distribute it to the powers. For example:
(4 * 5)² = 20² = 400
Or, we can rewrite it like:
(4 * 5)² = 4² * 5² = 16 * 25 = 400
Now, onto the problem.
First, multiply the exponents with the one outside the parentheses.
a^(1/2 * 1/2) * b^(1/3 * 1/2)
Simplify.
a^(1/4) * b^(1/6)
So, the answer is D.
Just in case, let's double check the answer.
Let's pretend that a=16 and b=64.
Then,
(a^(1/2) * b^(1/3))^(1/2) = a^(1/4) * b^(1/6)
(16^(1/2) * 64^(1/3))^(1/2) = 16^(1/4) * 64^(1/6)
(4 * 4) ^ (1/2) = 2 * 2
16 ^ (1/2) = 4
4 = 4
Thus, the answer is correct.
