Answer
$1.496037119 \times 10^{11}$ (meters)
Work Step by Step
Given the formula:
$D = \left(\dfrac{GM}{4\pi^{2}} \right)^{1/3} T^{2/3}$
Given the values:
$G = 6.67 \times 10^{-11}$ (the gravitational constant).
$M = 1.99 \times 10^{30}$ (the mass of the sun).
$T = 365.25 \times 24 \times 60 \times 60$ ($1$ year on earth assuming the length of it is $365.25$ days in seconds).
We now just fill the given data with their respective variables forming this equation:
$D=((6.67 \times 10^{-11} \times 1.99 \times 10^{30})\div(4 \times \pi^{2}) )^{1\div3} \times (365.25 \times 24 \times 60 \times 60)^{2\div3}$
which in the end will result to $1.496037119 \times 10^{11}$ (meters).
