Simplify completely 25 w to the sixth power over 10 w to the third power divided by 30 w squared over 5 w.

25 w to the sixth power over 10 w to the third power divided by 30 w squared over 5 w.

25w⁶ / 10w³  ÷ 30w² / 5w

Get the reciprocal of the 2nd fraction and multiply it with the 1st fraction

25w⁶ / 10w³   * 5w / 30w² → 25w⁶ * 5w / 10w³ * 30w² = 125w⁷ / 300w⁵ 

*When you multiply exponents with the same base, you simply add them.
w⁶ * w = w⁶⁺¹ = w⁷
w³ * w² = w³⁺² = w⁵

Cancel out w⁵
125w⁷ / 300w5 = 125w² / 300

Simplify the constant:
125 / 25 = 5
300 / 25 = 12

5w² / 12    is the simplified form of the given equation.