Let a₁ , a₂ , a₃ , a₄ , a₅ be 5 gepmetric means between a = 576 and b = 9

So, the sequence a, a₁ , a₂ , a₃ , a₄ , a₅ , b is in GP

Now, common ratio r = (b/a)^{1/(n + 1)}

=> r = (9/576)^{1/(5 + 1)}

=> r = (1/64)^1/6

=> r = (1/2⁶ )^1/6

=> r = 1/2

Now, a₁ = ar = 576 * (1/2) = 576/2 = 288

a₂ = ar² = 576 * (1/2)² = 576/4 = 144

a₃ = ar³ = 576 * (1/2)³ = 576/8 = 72

a₄ = ar⁴ = 576 * (1/2)⁴ = 576/16 = 36

a₅ = ar⁵ = 576 * (1/2)⁵ = 576/32 = 18

So, 288, 144, 72, 36, 18 are the 5 geometric means inserted between 576 and 9