Which expression is equivalent to (144k^2r^14)^1/2 for all positive values of k and r?
F. 12kr^7
G. 72k^2r^14
H. 144kr^3
J. 12k^2r^14
To simplify the expression, we will consider each term separately.
First, take the square root of 144, which is $\sqrt{144} = 12$.
Next, divide the exponents of each variable term by 2:
$k^{2/2} = k$ and $r^{14/2} = r^7$.
Therefore, the simplified expression is $12kr^7$.
Hence, the answer is $\boxed{\text{(F) }12kr^7}$.