A number to the 10th power divided by the same number to the 7th power equals 512. What is the number? The number is

Question (rewritten into a easier form): x¹⁰ ÷ x⁷ = 512

Using our knowledge that x¹⁰ ÷ x⁷ = x³, we can rewrite the equation as:

x³ = 512

To work out what x is, we do ∛512 (cubed root of 512).

This will get us: 8.

Final

The number is 8.

Proof:

8¹⁰ = 1073741824
8⁷ = 2097152

1073741824 ÷ 2097152 = 512

I hope this made sense and helped, if you have any questions or you think I made a mistake please let me know!

:)