Kepler's law: distance to moon from Earth

using (T^2)/(R^3)=(4pi^2)/GM, find distance from moon to Earth

here's what I have
G=6.67*10^-11
M=5.97*10^24 (mass of Earth)
T=27.3 days=2.36*10^6 s (period of moon)
r=?

I keep getting 1.8533333e+31 and it should be around 384,400 m

Whoa horse...the Moon is farther than 384 km from my house...that's the 384,000 m you wrote.

So the plug and chug, given your numbers is, R = ((G\M T^2)/(4 pi^2))^(1/3) = ((6.67E-11*5.97E24*(2.34E6)^2)/(4*pi()^2… = 380823769.7 m. ANS. About 381,000 km (not m).

To memorize Kepler's 3rd Law (K3L) of Planetary Motion, I always use the "1-2-3" (referring to the exponents on M, ω, and a) form of it *:

GM = ω²a³

which, along with
ωT = 2π, a = R

gives the form you have:
T²/R³ = 4π²/(GM)

Then solve for R:
R³ = GMT²/(4π²) = 6.67•10ˉ¹¹m³/(kg•s²) • 5.97•10²⁴kg • 2.36²•10¹²s² / 39.478
= 221.8•10²⁵m³ / 39.478 = 5.618•10²⁵m³ = 56.18•10²⁴m³
R ≈ 3.83•10⁸m = 383,000 km [You forgot the "k" in your "should be" answer.]

distance to the moon is 384,400 KM

you have to change them to meters..

so its 3.84*10^8 m